各图书bug修改

闫增涛

2024-11-19 d8c24a06b3e7844ad65e7c821c022dbb36d29430

 src/books/mathBook/view/components/chapter002.vue

@@ -1,22 +1,72 @@
<template>
  <div class="chapter" num="3">

    <!-- 第二单元首页 -->
    <div class="page-box" page="38">
      <div v-if="showPageList.indexOf(38) > -1">

        <div class="padding-116">第二单元首页</div>
        <h1 id="a006">
          <img class="img-0" alt="" src="../../assets/images/dy2.jpg" />
        </h1>
        <div class="padding-116">
          <p>
            物体有轻有重，速度有快有慢，气温有高有低，光线有强有弱，面积有大有小……在实际生活中，这种不相等的数量关系无处不在.我们可以利用不等关系构建不等式，并通过不等式解决现实生活中的问题.
          </p>
          <p>
            例如，随着时代的进步，人们对住宅的要求越来越高.通常人们在选择住宅时，都会考虑采光问题，这就需要把窗户开得尽可能大.按采光标准，窗户的有效透光面积与室内地面面积的比值应不小于
            <math display="0">
              <mfrac>
                <mn>1</mn>
                <mn>7</mn>
              </mfrac>
            </math>，这个比值越大，住宅的采光效果越好.
          </p>
          <p>
            如果窗户的有效透光面积和室内地面面积同时增加相同的面积，是不是采光效果就会更好呢？解决这样的问题就需要用到有关不等式的知识.
          </p>
          <p>
            不等式是数学中的重要内容，它具有应用广泛、变换灵活的特点，是研究数量大小关系的必备知识，与数学的其他分支内容有着密切的联系，也是学习高等数学的基础和工具.
          </p>
          <p>
            本单元在初中学习的基础之上，进一步学习不等式的基本性质、区间、一元二次不等式、含绝对值的不等式等.学习根据数量关系列出相应的不等式，并利用这些不等式找到问题的解决方案，提升数学运算、直观想象、逻辑推理和数学建模等核心素养.
          </p>
        </div>
      </div>
    </div>
    <!-- 目标 -->
    <div class="page-box" page="39">
      <div v-if="showPageList.indexOf(39) > -1">
        <div class="padding-116">目标</div>
        <div class="padding-116">
          <p class="left">
            <img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
          </p>
          <div class="fieldset">
            <p>1.不等式的基本性质.</p>
            <p>（1） 掌握判断两个数（式）大小的“作差比较法”；</p>
            <p>（2） 了解不等式的基本性质.</p>
            <p>2.区间.</p>
            <p>理解区间的概念.</p>
            <p>3.一元二次不等式.</p>
            <p>（1） 了解一元二次不等式的概念；</p>
            <p>
              （2） 了解二次函数、一元二次方程与一元二次不等式三者之间的关系；
            </p>
            <p>（3） 掌握一元二次不等式的解法.</p>
            <p>4.含绝对值的不等式.</p>
            <p>
              （1）
              了解含绝对值的不等式|<i>x</i>|＜<i>a</i>和|<i>x</i>|＞<i>a</i>（<i>a</i>＞0）的含义；
            </p>
            <p>
              （2）
              掌握形如|<i>ax</i>+<i>b</i>|＜<i>c</i>和|<i>ax</i>+<i>b</i>|＞<i>c</i>（<i>c</i>＞0）的不等式的解法.
            </p>
            <p>5.不等式的应用.</p>
            <p>
              初步掌握从实际问题中抽象出一元二次不等式模型解决简单实际问题的方法.
            </p>
          </div>
        </div>
      </div>
    </div>



    <!-- 033 -->
    <div class="page-box" page="40">
      <div v-if="showPageList.indexOf(40) > -1">
@@ -28,10 +78,153 @@
            <p><span>033</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="left">
            <img class="inline2" alt="" src="../../assets/images/xxmb.jpg" />
          </p>
          <div class="fieldset">
            <p>1.不等式的基本性质.</p>
            <p>（1） 掌握判断两个数（式）大小的“作差比较法”；</p>
            <p>（2） 了解不等式的基本性质.</p>
            <p>2.区间.</p>
            <p>理解区间的概念.</p>
            <p>3.一元二次不等式.</p>
            <p>（1） 了解一元二次不等式的概念；</p>
            <p>
              （2） 了解二次函数、一元二次方程与一元二次不等式三者之间的关系；
            </p>
            <p>（3） 掌握一元二次不等式的解法.</p>
            <p>4.含绝对值的不等式.</p>
            <p>
              （1）
              了解含绝对值的不等式|<i>x</i>|＜<i>a</i>和|<i>x</i>|＞<i>a</i>（<i>a</i>＞0）的含义；
            </p>
            <p>
              （2）
              掌握形如|<i>ax</i>+<i>b</i>|＜<i>c</i>和|<i>ax</i>+<i>b</i>|＞<i>c</i>（<i>c</i>＞0）的不等式的解法.
            </p>
            <p>5.不等式的应用.</p>
            <p>
              初步掌握从实际问题中抽象出一元二次不等式模型解决简单实际问题的方法.
            </p>
          </div>
          <h2 id="b007">
            2.1 不等式的基本性质<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
          </h2>
          <h3 id="c012">
            2.1.1 不等式的基本性质<span class="fontsz2">＞＞＞</span>
          </h3>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
              </p>
            </div>
            <p class="block">我们知道：</p>
            <p class="block">（1） <i>a</i>＞<i>b</i>⇔<i>a</i>-<i>b</i>＞0；</p>
            <p class="block">（2） <i>a</i>＞<i>b</i>⇔<i>b</i>＜<i>a</i>；</p>
            <p class="block">
              （3）
              若<i>a</i>＞<i>b</i>，<i>b</i>＞<i>c</i>，则<i>a</i>＞<i>c</i>.
            </p>
            <p class="block">初中我们还学习过不等式的下列性质：</p>
            <p class="block">
              <b>性质1</b>
              <i>a</i>＞<i>b</i>⇔<i>a</i>±<i>c</i>＞<i>b</i>±<i>c</i>.
            </p>
            <p class="block">
              <b>性质2</b>
              <i>a</i>＞<i>b</i>，<i>c</i>＞0⇒<i>ac</i>＞<i>bc</i>（或<math display="0">
                <mfrac>
                  <mi>a</mi>
                  <mi>c</mi>
                </mfrac>
                <mo>＞</mo>
                <mfrac>
                  <mi>b</mi>
                  <mi>c</mi>
                </mfrac>
              </math>）.
            </p>
            <p class="block">
              <b>性质3</b>
              <i>a</i>＞<i>b</i>，<i>c</i>＜0⇒<i>ac</i>＜<i>bc</i>（或<math display="0">
                <mfrac>
                  <mi>a</mi>
                  <mi>c</mi>
                </mfrac>
                <mo>＜</mo>
                <mfrac>
                  <mi>b</mi>
                  <mi>c</mi>
                </mfrac>
              </math>）.
            </p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/wttc.jpg" /></p>
          <p>
            有观点认为，最美人体的下半身长（肚脐至脚的触地点的长度）与全身长之比是<math display="0">
              <mfrac>
                <mrow>
                  <msqrt>
                    <mn>5</mn>
                  </msqrt>
                  <mo>−</mo>
                  <mn>1</mn>
                </mrow>
                <mn>2</mn>
              </mfrac>
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mfrac>
                  <mrow>
                    <msqrt>
                      <mn>5</mn>
                    </msqrt>
                    <mo>−</mo>
                    <mn>1</mn>
                  </mrow>
                  <mn>2</mn>
                </mfrac>
                <mo>≈</mo>
                <mn>0.618</mn>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，这被称为黄金分割比例.某芭蕾舞演员全身长166cm，下半身长98cm.表演过程中，芭蕾舞演员会立起脚尖跳舞，此时肚脐与脚的触地点的距离增加了8
            cm.试问：该芭蕾舞演员下半身长与全身长的比值，在脚尖立起前后哪个大？
            哪一个更接近0.618？
          </p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            该芭蕾舞演员脚尖立起前，下半身长与全身长的比值为<math display="0">
              <mfrac>
                <mn>98</mn>
                <mn>166</mn>
              </mfrac>
            </math>；脚尖立起后，下半身长与全身长的比值为<math display="0">
              <mfrac>
                <mrow>
                  <mn>98</mn>
                  <mo>+</mo>
                  <mn>8 </mn>
                </mrow>
                <mrow>
                  <mn>166</mn>
                  <mo>+</mo>
                  <mn>8</mn>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mfrac>
                <mn>106</mn>
                <mn>174</mn>
              </mfrac>
            </math>
            .本题要求比较这两个分数的大小.
          </p>
        </div>
      </div>
    </div>

    <!-- 034 -->
    <div class="page-box" page="41">
      <div v-if="showPageList.indexOf(41) > -1">
@@ -40,8 +233,112 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
          <p>
            为了借助不等式知识解决上面的问题，我们需要进一步研究不等式的性质.根据初中学过的不等式的3个基本性质，可以得到一系列推论.
          </p>
          <p>根据性质1，可得下列推论.</p>
          <p>
            <b>推论1</b>
            <i>a</i>＞<i>b</i>，<i>c</i>＞<i>d</i>⇒<i>a</i>+<i>c</i>＞<i>b</i>+<i>d</i>.
          </p>
          <p><b>证明</b> 根据性质1，可知</p>
          <p class="center">
            <i>a</i>＞<i>b</i>⇒<i>a</i>+<i>c</i>＞<i>b</i>+<i>c</i>，
          </p>
          <p class="center">
            <i>c</i>＞<i>d</i>⇒<i>c</i>+<i>b</i>＞<i>d</i>+<i>b</i>，即<i>b</i>+<i>c</i>＞<i>b</i>+<i>d</i>.
          </p>
          <p>
            从而<i>a</i>+<i>c</i>＞<i>b</i>+<i>c</i>＞<i>b</i>+<i>d</i>，即<i>a</i>+<i>c</i>＞<i>b</i>+<i>d</i>.
          </p>
          <p>例如，5＞1，3＞-2，根据推论1，有5+3＞1+（-2），即8＞-1.</p>
          <p>
            <b>推论2</b> <i>a</i>+<i>b</i>＞<i>c</i>⇒<i>a</i>＞<i>c</i>-<i>b</i>.
          </p>
          <p>根据性质2，可得下列推论.</p>
          <p>
            <b>推论3</b>
            <i>a</i>＞<i>b</i>＞0，<i>c</i>＞<i>d</i>＞0⇒<i>ac</i>＞<i>bd</i>.
          </p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[41]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
          <p>
            <span class="zt-ls"><b>例1</b></span>　已知<i>a</i>＞<i>b</i>＞0.
          </p>
          <p class="p-btn">
            （1） 比较2a与2b的大小；
            <span class="btn-box" @click="isShowAnswer0 = !isShowAnswer0">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer0">
            <span class="zt-ls"><b>解</b></span>（1） 因为<i>a</i>＞<i>b</i>，2＞0，根据性质2，有2<i>a</i>＞2<i>b</i>.
          </p>
          <p class="p-btn">
            （2） 比较-2a与-2b的大小；
            <span class="btn-box" @click="isShowAnswer1 = !isShowAnswer1">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer1">
            <span class="zt-ls"><b>解</b></span>
            （2）
            因为<i>a</i>＞<i>b</i>，-2＜0，根据性质3，有-2<i>a</i>＜-2<i>b</i>.
          </p>
          <p class="p-btn">
            （3） 比较ac与bc的大小.
            <span class="btn-box" @click="isShowAnswer2 = !isShowAnswer2">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer2">
            <p>
              <span class="zt-ls"><b>解</b></span>
              （3） 若<i>c</i>＞0，根据性质2，有<i>ac</i>＞<i>bc</i>.
            </p>
            <p>若<i>c</i>＜0，根据性质3，有<i>ac</i>＜<i>bc</i>.</p>
            <p>若<i>c</i>=0，则有<i>ac</i>=<i>bc</i>=0，所以<i>ac</i>=<i>bc</i>.</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span class="t1">已知a＞b，比较a-1与b-2的大小.</span>
            <span class="btn-box" @click="isShowAnswer3 = !isShowAnswer3">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer3">
            <p>
              <span class="zt-ls"><b>解</b></span> 因为<i>a</i>＞<i>b</i>，-1＞-2，
            </p>
            <p>根据推论1，有<i>a</i>+（-1）＞<i>b</i>+（-2），</p>
            <p>即<i>a</i>-1＞<i>b</i>-2.</p>
          </div>
        </div>
      </div>
    </div>
    <!-- 035 -->
@@ -55,7 +352,167 @@
            <p><span>035</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[42]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
          <h3 id="c013">2.1.2 作差比较法<span class="fontsz2">＞＞＞</span></h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            我们知道实数可以比较大小.数学中经常用下面的等价关系比较<i>a</i>，<i>b</i>的大小.
          </p>
          <p class="center"><i>a</i>-<i>b</i>＞0⇔<i>a</i>＞<i>b</i>；</p>
          <p class="center"><i>a</i>-<i>b</i>＜0⇔<i>a</i>＜<i>b</i>；</p>
          <p class="center"><i>a</i>-<i>b</i>=0⇔<i>a</i>=<i>b</i>.</p>
          <p>
            由此可见，比较<i>a</i>，<i>b</i>的大小，只要判断它们的差<i>a</i>-<i>b</i>与0的大小关系即可.
          </p>
          <p>
            例如，我们可以作差比较<i>a</i><sup>2</sup>+1与2<i>a</i>的大小（<i>a</i>≠1）.
          </p>
          <p>
            因为（<i>a</i><sup>2</sup>+1）-2<i>a</i>=<i>a</i><sup>2</sup>-2<i>a</i>+1=（<i>a</i>-1）<sup>2</sup>，且当<i>a</i>≠1时，（<i>a</i>-1）<sup>2</sup>＞0，所以<i>a</i><sup>2</sup>+1＞2<i>a</i>.
          </p>
          <p class="p-btn">
            <span class="zt-ls"><b>例1</b></span>　
            <span class="t1">分析本节“问题提出”中的问题.</span>
            <span class="btn-box" @click="isShowAnswer4 = !isShowAnswer4">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer4">
            <p>
              <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mn>98</mn>
                    <mo>+</mo>
                    <mn>8</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>+</mo>
                    <mn>8</mn>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mn>98</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                    <mo>−</mo>
                    <mn>106</mn>
                    <mo>×</mo>
                    <mn>166</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mo>−</mo>
                    <mn>544</mn>
                  </mrow>
                  <mrow>
                    <mn>166</mn>
                    <mo>×</mo>
                    <mn>174</mn>
                  </mrow>
                </mfrac>
                <mo>＜</mo>
                <mn>0</mn>
              </math>，所以<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>＜</mo>
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
              </math>.
            </p>
            <p>
              又因为<math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>≈</mo>
                <mn>0.590</mn>
                <mn>4</mn>
              </math>，<math display="0">
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>≈</mo>
                <mn>0.690</mn>
                <mn>2</mn>
              </math>，所以立起脚尖后，该芭蕾舞演员的下半身长与全身长的比值更接近0.618.
            </p>
          </div>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
              </p>
            </div>
            <p class="block">
              本例中，作差时也可以这样计算：
              <math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>=</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mn>1</mn>
                  <mo>−</mo>
                  <mfrac>
                    <mn>68</mn>
                    <mn>166</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>-</mo>
              </math>
            </p>
          </div>
        </div>
      </div>
    </div>
    <!-- 036 -->
@@ -66,7 +523,264 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <div class="bk">
            <p class="block">
              <math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mn>1</mn>
                  <mo>−</mo>
                  <mfrac>
                    <mn>68</mn>
                    <mn>174</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
                <mo>=</mo>
                <mfrac>
                  <mn>68</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mn>68</mn>
                  <mn>166</mn>
                </mfrac>
              </math>
              .因为分子相同时，分母越大，分数越小，所以
              <math display="0">
                <mfrac>
                  <mn>98</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mn>106</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mn>68</mn>
                  <mn>174</mn>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mn>68</mn>
                  <mn>166</mn>
                </mfrac>
                <mo>＜</mo>
                <mn>0</mn>
              </math>.
            </p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span calss="t1">已知b＞a＞0，c＞0，比较</span>
            <math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mrow>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
              </mfrac>
            </math>与<math display="0">
              <mfrac>
                <mi>a</mi>
                <mi>b</mi>
              </mfrac>
            </math>的大小.
            <span class="btn-box" @click="isShowAnswer5 = !isShowAnswer5">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer5">
            <p>
              <span class="zt-ls"><b>解</b></span> 作差可得<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mi>a</mi>
                  <mi>b</mi>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>a</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                  </mrow>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                  </mrow>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                  </mrow>
                  <mrow>
                    <mi>b</mi>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                  </mrow>
                </mfrac>
                <mo>=</mo>
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>−</mo>
                      <mi>a</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                  </mrow>
                </mfrac>
              </math>.
            </p>
            <p>
              因为<i>b</i>＞<i>a</i>＞0，所以<i>b</i>-<i>a</i>＞0.又因为<i>c</i>＞0，所以<math display="0">
                <mfrac>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>−</mo>
                      <mi>a</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mrow data-mjx-texclass="INNER">
                      <mo data-mjx-texclass="OPEN">(</mo>
                      <mi>b</mi>
                      <mo>+</mo>
                      <mi>c</mi>
                      <mo data-mjx-texclass="CLOSE">)</mo>
                    </mrow>
                    <mi>b</mi>
                  </mrow>
                </mfrac>
                <mo>＞</mo>
                <mn>0</mn>
              </math>，
            </p>
            <p>
              即<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                </mfrac>
                <mo>−</mo>
                <mfrac>
                  <mi>a</mi>
                  <mi>b</mi>
                </mfrac>
                <mo>＞</mo>
                <mn>0</mn>
              </math>，所以<math display="0">
                <mfrac>
                  <mrow>
                    <mi>a</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                  <mrow>
                    <mi>b</mi>
                    <mo>+</mo>
                    <mi>c</mi>
                  </mrow>
                </mfrac>
                <mo>＞</mo>
                <mfrac>
                  <mi>a</mi>
                  <mi>b</mi>
                </mfrac>
              </math>.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[43] ? questionData[43][1] : []" :hideCollect="true" sourceType="json"
              v-if="questionData">
            </examinations>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[43] ? questionData[43][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 037 -->
@@ -80,7 +794,37 @@
            <p><span>037</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <h3 id="c014">习题2.1<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[44]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
          <h2 id="b008">2.2 区间<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/gn.jpg" /></p>
            </div>
            <p class="block">闭区间</p>
            <p class="block">开区间</p>
            <p class="block">左闭右开区间</p>
            <p class="block">左开右闭区间</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            以不等式表示元素共同特征的数集，还有一种更为简单的表示方法，叫<b>作区间表示法</b>.
          </p>
          <p>设<i>a</i>＜<i>b</i>，我们规定：</p>
          <p>
            （1）
            满足不等式<i>a</i>≤<i>x</i>≤<i>b</i>的<i>x</i>的集合叫作<b>闭区间</b>，表示为
            ［<i>a</i>，<i>b</i>］.
          </p>
          <p>
            （2）
            满足不等式<i>a</i>＜<i>x</i>＜<i>b</i>的<i>x</i>的集合叫作<b>开区间</b>，表示为（<i>a</i>，<i>b</i>）.
          </p>
        </div>
      </div>
    </div>
    <!-- 038 -->
@@ -91,7 +835,27 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p>
            （3）
            满足不等式<i>a</i>≤<i>x</i>＜<i>b</i>和<i>a</i>＜<i>x</i>≤<i>b</i>的<i>x</i>的集合分别叫作<b>左闭右开区间</b>和<b>左开右闭区间</b>，分别表示为
            ［<i>a</i>，<i>b</i>），（<i>a</i>，<i>b</i>］.
          </p>
          <p>
            这里的<i>a</i>与<i>b</i>都叫作相应区间的端点.这些区间还可以用数轴表示（如表2-1所示）.在数轴上，用实心点表示包括在区间内的端点，用空心点表示不包括在区间内的端点.
          </p>
          <p class="img">表2-1</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0049-1.jpg" /></p>
          <p>
            实数集<b>R</b>可以用区间表示为（-∞，+∞）.符号“∞”读作“无穷大”，它不是一个具体的数，仅表示某个量在变化时，绝对值无限增大的趋势.“+∞”读作“正无穷大”，表示某个量沿正方向无限增大；“-∞”读作“负无穷大”，表示某个量沿负方向无限变化，其绝对值无限增大.
          </p>
          <p>
            我们还可以把满足<i>x</i>≥<i>a</i>，<i>x</i>＞<i>a</i>，<i>x</i>≤<i>b</i>，<i>x</i>＜<i>b</i>的<i>x</i>的集合用区间分别表示为
            ［<i>a</i>，+∞），（<i>a</i>，+∞），（-∞，<i>b</i>］，（-∞，<i>b</i>），如表2-2所示.
          </p>
          <p class="img">表2-2</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0049-2.jpg" /></p>
        </div>
      </div>
    </div>
    <!-- 039 -->
@@ -102,36 +866,221 @@
            <p>第二单元 不等式</p>
          </li>
          <li>
            <p><span>039</span></p>
            <p><span>039-041</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <div class="bk mt-80">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
              </p>
            </div>
            <p class="block">
              区间也是一个集合，它是实数集的一个子集.但并非所有的数集都能用区间表示.例如，集合{1，3，4，5，7，8，11，12}、自然数集<b>N</b>、整数集<b>Z</b>就不能用区间表示.
            </p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例1</b></span>
            <span class="t1">把下列集合用区间表示出来，并指出区间的类型.</span>
            <span class="btn-box" @click="isShowAnswer6 = !isShowAnswer6">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p>（1） {<i>x</i>|-3≤<i>x</i>≤1}；（2） {<i>x</i>|-1＜<i>x</i>＜2}；</p>
          <p>
            （3）
            <math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mi>x</mi>
                <mrow>
                  <mo stretchy="false">|</mo>
                </mrow>
                <mfrac>
                  <mn>3</mn>
                  <mn>2</mn>
                </mfrac>
                <mo>≤</mo>
                <mi>x</mi>
                <mo>＜</mo>
                <mn>4</mn>
                <mo data-mjx-texclass="CLOSE">}</mo>
              </mrow>
            </math>；（4）
            <math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">{</mo>
                <mi>x</mi>
                <mrow>
                  <mo stretchy="false">|</mo>
                </mrow>
                <mo>−</mo>
                <mn>6</mn>
                <mo>＜</mo>
                <mi>x</mi>
                <mo>≤</mo>
                <mo>−</mo>
                <mfrac>
                  <mn>1</mn>
                  <mn>2</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">}</mo>
              </mrow>
            </math>；
          </p>
          <p>（5） {<i>x</i>|<i>x</i>≥2}；（6） {<i>x</i>|<i>x</i>＜1}.</p>
          <div v-if="isShowAnswer6">
            <p>
              <span class="zt-ls"><b>解</b></span>（1） ［-3，1］，是闭区间；
            </p>
            <p>（2）（-1，2），是开区间；</p>
            <p>
              （3）
              <math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">[</mo>
                  <mfrac>
                    <mn>3</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mn>4</mn>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，是左闭右开区间；
            </p>
            <p>
              （4）
              <math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mn>6</mn>
                  <mo>，</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">]</mo>
                </mrow>
              </math>，是左开右闭区间；
            </p>
            <p>（5） ［2，+∞），是左闭右开区间；</p>
            <p>（6）（-∞，1），是开区间.</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例2</b></span>
            <span class="t1">用区间表示不等式3<i>x</i>＜9<i>x</i>+4的解集，并在数轴上表示出来.</span>
            <span class="btn-box" @click="isShowAnswer7 = !isShowAnswer7">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer7">
            <p>
              <span class="zt-ls"><b>解</b></span> 解不等式3<i>x</i>＜9<i>x</i>+4，得
            </p>
            <math display="block">
              <mi>x</mi>
              <mo>＞</mo>
              <mo>−</mo>
              <mfrac>
                <mn>2</mn>
                <mn>3</mn>
              </mfrac>
              <mo>.</mo>
            </math>
            <p>
              所以不等式的解集用区间表示为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>2</mn>
                    <mn>3</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mo>+</mo>
                  <mi mathvariant="normal">∞</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，表示在数轴上如图2-1所示.
            </p>
            <p class="center"><img class="img-f" alt="" src="../../assets/images/0050-7.jpg" /></p>
            <p class="img">图2-1</p>
          </div>
          <p class="p-btn">
            <span class="zt-ls"><b>例3</b></span>
            <span class="t1">设<b>R</b>为全集，集合A={x|-5＜x＜6}，B={x|x≥3或x≤-3}，用区间表示A∩B.</span>　
            <span class="btn-box" @click="isShowAnswer8 = !isShowAnswer8">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer8">
            <p>
              <span class="zt-ls"><b>解</b></span>
              在数轴上将集合<i>A</i>，<i>B</i>表示出来，如图2-2所示.
            </p>
            <p class="center"><img class="img-d" alt="" src="../../assets/images/0050-8.jpg" /></p>
            <p class="img">图2-2</p>
            <p>
              <i>A</i>∩<i>B</i>={<i>x</i>|-5＜<i>x</i>＜6}∩{<i>x</i>|<i>x</i>≥3或<i>x</i>≤-3}
            </p>
            <p>={<i>x</i>|-5＜<i>x</i>≤-3}∪{<i>x</i>|3≤<i>x</i>＜6}</p>
            <p>=（-5，-3］∪［3，6）.</p>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations :cardList="questionData[47] ? questionData[47][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h3 id="c015">习题2.2<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[47] ? questionData[47][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h2 id="b009">
            2.3 一元二次不等式<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
          </h2>
          <h3 id="c016">
            2.3.1 一元二次不等式的概念<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/wttc.jpg" /></p>
          <p class="center"><b>汽车急刹车的停车距离</b></p>
          <p>
            随着人民生活质量的提高，人们的购车意愿上升.2021年末全国民用汽车保有量30
            151万辆，比2020年末增加2
            064万辆.在此背景下，汽车行驶安全越发需要引起人们的重视。汽车行驶的过程中，由于惯性的作用，急刹车后会继续向前滑行一段距离才能停住，一般称这段距离为汽车“急刹车的停车距离”.急刹车的停车距离<i>y</i>（m）
            与车速<i>x</i>（km/h）之间具有确定的关系.不同车型的汽车急刹车的停车距离与车速之间的关系不同，同一车型的汽车急刹车的停车距离与车速之间的关系也会因为天气条件、道路状况等因素的不同而发生变化.
          </p>
          <p>
            在正常天气条件下，某汽车在高速公路上急刹车的停车距离<i>y</i>（m）
            与车速<i>x</i>（km/h）
            之间的函数关系为<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>，如果希望该汽车急刹车的停车距离不
          </p>
        </div>
      </div>
    </div>
    <!-- 040 -->
    <div class="page-box" page="47">
      <div v-if="showPageList.indexOf(47) > -1">
        <ul class="page-header-odd fl al-end">
          <li>040</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
      </div>
    <div class="page-box hidePage" page="47">
    </div>
    <!-- 041 -->
    <div class="page-box" page="48">
      <div v-if="showPageList.indexOf(48) > -1">
        <ul class="page-header-box">
          <li>
            <p>第二单元 不等式</p>
          </li>
          <li>
            <p><span>041</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
      </div>
    <div class="page-box hidePage" page="48">
    </div>
    <!-- 042 -->
    <div class="page-box" page="49">
@@ -141,7 +1090,58 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="t0">
            超过50m，那么其行驶速度的范围是多少？（注：高速公路上的最低速度为60
            km/h）
          </p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            上述问题要求“汽车急刹车的停车距离不超过50
            m”，即y≤50.而该汽车急刹车的停车距离与车速之间的关系为<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>，因此得到
          </p>
          <p class="center">0.007<i>x</i><sup>2</sup>+0.2<i>x</i>≤50.</p>
          <p>
            为了求出行驶速度的范围，我们需要对这个不等式进行求解.这个不等式可以进一步整理为
          </p>
          <p class="center">0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50≤0.</p>
          <p>
            这个不等式只含有一个未知数<i>x</i>，并且未知数<i>x</i>的最高次数为2.像这样的不等式还有很多，如2<i>x</i><sup>2</sup>+5<i>x</i>-3＜0，3<i>x</i><sup>2</sup>+6<i>x</i>-1＞0等.
          </p>
          <div class="bk">
            <div class="bj1">
              <p class="left"><img class="img-gn1" alt="" src="../../assets/images/gn.jpg" /></p>
            </div>
            <p class="block">一元二次不等式</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
          <p>
            一般地，只含有一个未知数，且未知数的最高次数为2的整式不等式，叫作<b>一元二次不等式</b>.一元二次不等式的一般表达式为<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0（≥0）或<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0（≤0），其中<i>a</i>，<i>b</i>，<i>c</i>均为常数，且<i>a</i>≠0.
          </p>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
              </p>
            </div>
            <p class="block"><b>1.一元二次方程</b></p>
            <p class="block">
              一元二次方程<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>=0（<i>a</i>≠0）的实数解的情况与求解公式如表2-3所示.
            </p>
            <p class="img">表2-3</p>
            <p class="center">
              <img class="img-a" alt="" src="../../assets/images/0053-1.jpg" />
            </p>
            <p class="block">
              当<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>＞0时，有些一元二次方程也可以用因式分解法写成<i>a</i>（<i>x</i>-<i>x</i>1）（<i>x</i>-<i>x</i>2）=0（<i>a</i>≠0），然后再求解.
            </p>
            <p class="block"><b>2.二次函数</b></p>
            <p class="block">
              二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>（<i>a</i>≠0）的图像是一条抛物线.当<i>a</i>＞0时，抛物线开口向上；当<i>a</i>＜0时，抛物线开口向下.抛物线与<i>x</i>轴共有3种
              位置关系.
            </p>
          </div>
        </div>
      </div>
    </div>
    <!-- 043 -->
@@ -155,7 +1155,199 @@
            <p><span>043</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <div class="bk">
            <p class="block">
              （1） 当<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>＞0时，抛物线与<i>x</i>轴有两个交点；
            </p>
            <p class="block">
              （2） 当<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=0时，抛物线与<i>x</i>轴只有一个交点；
            </p>
            <p class="block">
              （3） 当<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>＜0时，抛物线与<i>x</i>轴无交点.
            </p>
            <p class="block">抛物线与<i>x</i>轴的3种位置关系如表2-4所示.</p>
            <p class="img">表2-4</p>
            <p class="center">
              <img class="img-a" alt="" src="../../assets/images/0054-1.jpg" />
            </p>
            <p class="block">
              二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>（<i>a</i>≠0）的图像的对称轴方程为<math display="0">
                <mi>x</mi>
                <mo>=</mo>
                <mo>−</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
                    <mn>2</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
              </math>，顶点坐标为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mi>b</mi>
                    <mrow>
                      <mn>2</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo>，</mo>
                  <mfrac>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                      <mi>c</mi>
                      <mo>−</mo>
                      <msup>
                        <mi>b</mi>
                        <mrow>
                          <mn>2</mn>
                        </mrow>
                      </msup>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，与<i>y</i>轴的交点坐标为（0，<i>c</i>）.
            </p>
          </div>
          <p class="p-btn">
            <b>例</b>
            <span>已知二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3，</span>
            <span class="btn-box" @click="openDialog(thinkOne)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="p-btn">
            （1） 画出该函数图像；
            <span class="btn-box" @click="isShowAnswer9 = !isShowAnswer9">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer9">
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0055-1.jpg" /></p>
            <p class="img">图2-3</p>
            <p>
              <span class="zt-ls"><b>解</b></span>（1） 因为<i>a</i>=1＞0，所以函数图像为开口向上的抛物线.
            </p>
            <p>
              因为<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×（-3）=16＞0，
            </p>
            <p>
              所以一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0有两个不相等的实数解.
            </p>
            <p>解方程，得<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3.</p>
            <p>所以抛物线与<i>x</i>轴的交点坐标为（-1，0），（3，0）.</p>
            <p>
              抛物线的顶点坐标为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mi>b</mi>
                    <mrow>
                      <mn>2</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo>，</mo>
                  <mfrac>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                      <mi>c</mi>
                      <mo>−</mo>
                      <msup>
                        <mi>b</mi>
                        <mrow>
                          <mn>2</mn>
                        </mrow>
                      </msup>
                    </mrow>
                    <mrow>
                      <mn>4</mn>
                      <mi>a</mi>
                    </mrow>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>，即（1，-4）.
            </p>
            <p>
              抛物线的对称轴方程为<math display="0">
                <mi>x</mi>
                <mo>=</mo>
                <mo>−</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
                    <mn>2</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
              </math>，即<i>x</i>=1.抛物线与<i>y</i>轴的交点坐标为（0，<i>c</i>），即（0，-3）.根据函数的对称性，可以再取一些点，如（2，-3）.
            </p>
            <p>
              根据以上信息，就可以画出函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像（如图2-3所示）.
            </p>
          </div>
          <p class="p-btn">
            （2）
            指出该函数图像上纵坐标分别为y=0，y＞0，y＜0的所有点；
            <span class="btn-box" @click="isShowAnswer10 = !isShowAnswer10">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer10">
            <span class="zt-ls"><b>解</b></span>
            （2）
            观察图像可知，满足<i>y</i>=0的点是抛物线与<i>x</i>轴的交点；满足<i>y</i>＞0的点是抛物线在<i>x</i>轴上方的所有点；满足<i>y</i>＜0的点是抛物线在<i>x</i>轴下方的所有点.
          </p>
          <p class="p-btn">
            （3）
            根据函数图像写出y=0，y＞0，y＜0时所对应的x的值或取值范围.
            <span class="btn-box" @click="isShowAnswer11 = !isShowAnswer11">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer11">
            <p>
              <span class="zt-ls"><b>解</b></span>
              （3）
              观察图像可知，当<i>y</i>=0时，对应抛物线与<i>x</i>轴的两个交点，此时<i>x</i>有两个取值，<i>x</i><sub>1</sub>=-1，<i>x</i><sub>2</sub>=3；
            </p>
            <p>
              当<i>y</i>＞0时，对应抛物线在<i>x</i>轴上方的所有点，此时<i>x</i>的取值范围是<i>x</i>＜-1或<i>x</i>＞3；
            </p>
            <p>
              当<i>y</i>＜0时，对应抛物线在<i>x</i>轴下方的所有点，此时<i>x</i>的取值范围是-1＜<i>x</i>＜3.
            </p>
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    <!-- 044 -->
@@ -166,7 +1358,365 @@
          <li>数学.基础模块</li>
          <li>上册</li>
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                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
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            <examinations :cardList="questionData[51] ? questionData[51][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
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          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <p>已知下列二次函数：</p>
            <p>①<i>y</i>=<i>x</i><sup>2</sup>-3<i>x</i>-4， ②<i>y</i>=<i>x</i><sup>2</sup>+<i>x</i>+2，
              ③<i>y</i>=<i>x</i><sup>2</sup>-6<i>x</i>+9.</p>
            <p>（1） 分别画出它们的函数图像；</p>
            <paint :page="51" :imgUrl="this.config.activeBook.resourceUrl + '/images/a6fe3d63.png'" />
            <p>
              （2） 根据函数图像写出<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0时所对应的<i>x</i>的值或取值范围.
              <span class="btn-box" @click="isShowAnswer = !isShowAnswer">
                <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                  <path class="a"
                    d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                    transform="translate(-3327.144 15329)" />
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              <li>答案：</li>
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                    <mo>&#x2460;</mo>
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                  <mi>y</mi>
                  <mo>&gt;</mo>
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                  <mo>&#x65F6;&#xFF0C;</mo>
                  <mi>x</mi>
                  <mo>&lt;</mo>
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                  <mo>&#xFF0C;</mo>
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                  <mo>&#xFF1B;</mo>
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                  <mi>y</mi>
                  <mo>=</mo>
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                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
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                  <mn>1</mn>
                  <mo>,</mo>
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                  <mo stretchy="false">)</mo>
                  <mo>,</mo>
                  <mo stretchy="false">(</mo>
                  <mn>4</mn>
                  <mo>,</mo>
                  <mn>0</mn>
                  <mo stretchy="false">)</mo>
                  <mo>;</mo>
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&gt;</mo>
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                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                </math>
                <math display="block">
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
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                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
                  <mo>&#xFF0C;&#x5176;&#x4E2D;&#xFF0C;</mo>
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                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
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                  <mo>&lt;</mo>
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                  <mo>&#x6216;</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>&gt;</mo>
                  <mn>4</mn>
                  <mo>&#xFF1B;</mo>
                </math>
                <math display="block">
                  <mo>&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
                  <mn>0</mn>
                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
                  <mo stretchy="false">(</mo>
                  <msub>
                    <mi>x</mi>
                    <mrow>
                      <mn>0</mn>
                    </mrow>
                  </msub>
                  <mo>,</mo>
                  <mi>y</mi>
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                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
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                  <mo>&lt;</mo>
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                  <mo>&#xFF1B;</mo>
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                    <mo>&#x2461;</mo>
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                  <mi>y</mi>
                  <mo>=</mo>
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                  <mo>+</mo>
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                  <mo stretchy="false">(</mo>
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                    <mo stretchy="false">)</mo>
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                  <mo>&gt;</mo>
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                  <mo>&#xFF1B;</mo>
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                  <mo>&#x5F53;</mo>
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                  <mo>&gt;</mo>
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                  <mo>,</mo>
                  <mi>y</mi>
                  <mo stretchy="false">)</mo>
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                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
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                  <mo>&#x2208;</mo>
                  <mi>R</mi>
                  <mo>.</mo>
                </math>
                <math display="block">
                  <mrow>
                    <mo>&#x2462;</mo>
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                  <mi>y</mi>
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                  <mo>=</mo>
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                  <mo>&#x2212;</mo>
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                    <mo stretchy="false">)</mo>
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                  <mo>.</mo>
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                <math display="block">
                  <mo>&#x5F53;</mo>
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                  <mo>=</mo>
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                  <mo>&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
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                  <mi>y</mi>
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                  <mo>&#x65F6;&#xFF0C;&#x6240;&#x5BF9;&#x5E94;&#x7684;&#x70B9;&#x4E3A;</mo>
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                  <mo>,</mo>
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                  <mo stretchy="false">)</mo>
                </math>
                <math display="block">
                  <mo>&#xFF0C;&#x5176;&#x4E2D;</mo>
                  <msub>
                    <mi>x</mi>
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                  <mo>&#x2260;</mo>
                  <mn>3</mn>
                  <mo>&#xFF1B;&#x5F53;</mo>
                  <mi>y</mi>
                  <mo>&lt;</mo>
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                  <mo>&#x65F6;&#xFF0C;&#x6CA1;&#x6709;&#x5BF9;&#x5E94;&#x7684;&#x70B9;</mo>
                  <mo>.</mo>
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    <!-- 045 -->
@@ -180,7 +1730,184 @@
            <p><span>045</span></p>
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        <div class="padding-116">
          <h3 id="c017">
            2.3.2 一元二次不等式的基本解法<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            回到本节开头的问题，如何解不等式0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50≤0呢？
          </p>
          <p>
            当<i>x</i>变化时，不等式的左边可以看作<i>x</i>的二次函数<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50.这样解不等式0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50≤0的问题就可以转化为求二次函数<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50的图像上<i>y</i>≤0所对应点的<i>x</i>的取值范围问题.
          </p>
          <p>
            二次函数<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50的图像是开口向上的抛物线.因为<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（0.2）<sup>2</sup>-4×0.007×（-50）=1.44＞0，所以抛物线与<i>x</i>轴有两个交点，交点的横坐标是方程0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50=0的两个解，解方程0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50=0得<i>x</i>1=-100，<math
              display="0">
              <msub>
                <mi>x</mi>
                <mrow>
                  <mn>2</mn>
                </mrow>
              </msub>
              <mo>=</mo>
              <mfrac>
                <mn>500</mn>
                <mn>7</mn>
              </mfrac>
            </math>.所以图像与<i>x</i>轴的交点坐标为（-100，0），<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mfrac>
                  <mn>500</mn>
                  <mn>7</mn>
                </mfrac>
                <mo>，</mo>
                <mn>0</mn>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.对称轴方程为<math display="0">
              <mi>x</mi>
              <mo>=</mo>
              <mo>−</mo>
              <mfrac>
                <mi>b</mi>
                <mrow>
                  <mn>2</mn>
                  <mi>a</mi>
                </mrow>
              </mfrac>
              <mo>=</mo>
              <mo>−</mo>
              <mfrac>
                <mn>100</mn>
                <mn>7</mn>
              </mfrac>
            </math>，顶点坐标为<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mfrac>
                  <mi>b</mi>
                  <mrow>
                    <mn>2</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo>，</mo>
                <mfrac>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                    <mi>c</mi>
                    <mo>−</mo>
                    <msup>
                      <mi>b</mi>
                      <mrow>
                        <mn>2</mn>
                      </mrow>
                    </msup>
                  </mrow>
                  <mrow>
                    <mn>4</mn>
                    <mi>a</mi>
                  </mrow>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>，即<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">(</mo>
                <mo>−</mo>
                <mfrac>
                  <mn>100</mn>
                  <mn>7</mn>
                </mfrac>
                <mo>，</mo>
                <mo>−</mo>
                <mfrac>
                  <mn>360</mn>
                  <mn>7</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">)</mo>
              </mrow>
            </math>.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0056-6.jpg" /></p>
          <p class="img">图2-4</p>
          <p>
            故二次函数<i>y</i>=0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50的简图如图2-4所示.
          </p>
          <p>观察图像可知：</p>
          <p>
            当<i>y</i>=0时，对应抛物线与<i>x</i>轴的两个交点，此时<i>x</i>1=-100，<math display="0">
              <msub>
                <mi>x</mi>
                <mrow>
                  <mn>2</mn>
                </mrow>
              </msub>
              <mo>=</mo>
              <mfrac>
                <mn>500</mn>
                <mn>7</mn>
              </mfrac>
            </math>；
          </p>
          <p>
            当<i>y</i>＜0时，对应抛物线在<i>x</i>轴下方的所有点，此时<i>x</i>的取值范围是<math display="0">
              <mo>−</mo>
              <mn>100</mn>
              <mo>＜</mo>
              <mi>x</mi>
              <mo>＜</mo>
              <mfrac>
                <mn>500</mn>
                <mn>7</mn>
              </mfrac>
            </math>.
          </p>
          <p>
            故满足不等式0.007<i>x</i><sup>2</sup>+0.2<i>x</i>-50≤0的<i>x</i>所在的区间为<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">[</mo>
                <mo>−</mo>
                <mn>100</mn>
                <mo>，</mo>
                <mfrac>
                  <mn>500</mn>
                  <mn>7</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">]</mo>
              </mrow>
            </math>.
          </p>
          <p>
            考虑到高速公路上的最低速度为60km/h，如果希望该汽车急刹车的停车距离不超过50m，那么其行驶速度的范围是<math display="0">
              <mrow data-mjx-texclass="INNER">
                <mo data-mjx-texclass="OPEN">[</mo>
                <mn>60</mn>
                <mo>，</mo>
                <mfrac>
                  <mn>500</mn>
                  <mn>7</mn>
                </mfrac>
                <mo data-mjx-texclass="CLOSE">]</mo>
              </mrow>
            </math>，行驶速度的最大值为<math display="0">
              <mfrac>
                <mn>500</mn>
                <mn>7</mn>
              </mfrac>
              <mo>≈</mo>
              <mn>71</mn>
            </math>（km/h）.
          </p>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
          <p>
            一般地，使一元二次不等式成立的值叫作这个<b>一元二次不等式的解</b>.
          </p>
        </div>
      </div>
    </div>
    <!-- 046 -->
@@ -191,7 +1918,83 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="t0">
            一元二次不等式的所有解组成的集合，叫作这个<b>一元二次不等式的解集</b>.
          </p>
          <p>
            上面的情形表明，二次函数图像的开口方向及其与<i>x</i>轴的交点坐标，可以确定其对应的一元二次不等式的解集.
          </p>
          <p><b>例</b> 利用二次函数的图像解下列一元二次不等式.</p>
          <p class="p-btn" >
            <span>（1） -<i>x</i><sup>2</sup>+3<i>x</i>+4＜0；</span>
            <span class="btn-box" @click="isShowAnswer12 = !isShowAnswer12">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer12" >
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-1.jpg" /></p>
            <p class="img">图2-5</p>
            <p>
              <span class="zt-ls"><b>解</b></span>（1）
              Δ=<i>b</i><sup>2</sup>-4<i>ac</i>=3<sup>2</sup>-4×（-1）×4=25＞0，所以函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像与<i>x</i>轴有两个交点.解方程-<i>x</i><sup>2</sup>+3<i>x</i>+4=0可得，<i>x</i>1=-1，<i>x</i>2=4.
            </p>
            <p>
              函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像是开口向下的抛物线，与<i>x</i>轴的交点坐标是（-1，0），（4，0），函数<i>y</i>=-<i>x</i><sup>2</sup>+3<i>x</i>+4的图像如图2-5所示.
            </p>
          </div>
          <p class="p-btn" >
            <span>（2） <i>x</i><sup>2</sup>-2<i>x</i>+3＞0.</span>
            <span class="btn-box" @click="isShowAnswer13 = !isShowAnswer13">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer13" >
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0057-2.jpg" /></p>
            <p class="img">图2-6</p>
            <p>
              <span class="zt-ls"><b>解</b></span>
              观察图像可得，不等式-<i>x</i><sup>2</sup>+3<i>x</i>+4＜0的解集是（-∞，
              -1）∪（4， +∞）.
            </p>
            <p>
              （2）
              <i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-2）<sup>2</sup>-4×1×3=-8＜0，所以函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像与<i>x</i>轴无交点.
            </p>
            <p>
              函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>+3的图像是开口向上的抛物线，与<i>x</i>轴无交点，其简图如图2-6所示.
            </p>
            <p>
              观察图像可得，不等式<i>x</i><sup>2</sup>-2<i>x</i>+3＞0的解集为<b>R</b>.
            </p>
          </div>
          <iframe src="https://www.geogebra.org/calculator" frameborder="0" class="iframe-box"></iframe>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
              </p>
            </div>
            <p class="block">
              例（1）
              中，注意到不等式-<i>x</i><sup>2</sup>+3<i>x</i>+4＜0⇔<i>x</i><sup>2</sup>-3<i>x</i>-4＞0，从而可将问题转化成解不等式<i>x</i><sup>2</sup>-3<i>x</i>-4＞0，即当一元二次不等式的二次项系数为负数时，可以利用不等式的性质将不等式化成二次项系数为正数的一元二次不等式，再求解.
            </p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/tjfx.jpg" /></p>
          <p>
            通过上面的分析，发现二次函数的图像、一元二次方程的解、一元二次不等式的解集之间有着密切的联系，可以总结成表2-5.
          </p>
          <p class="img">表2-5</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0057-3.jpg" /></p>
        </div>
      </div>
    </div>
    <!-- 047 -->
@@ -205,8 +2008,35 @@
            <p><span>047</span></p>
          </li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="img">续表</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0058-1.jpg" /></p>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[54] ? questionData[54][1] : []" :hideCollect="true" sourceType="json"
              v-if="questionData">
            </examinations>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/cxgk.jpg" /></p>
          <p>
            一般地，与二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>（<i>a</i>＞0）对应的一元二次不等式有四种情形，分别是<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0，<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≥0，<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0，<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≤0.利用二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>（<i>a</i>＞0）的图像求解相应的一元二次不等式，可以分为三步.
          </p>
          <p>
            第一步：确定相应的一元二次方程<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>=0的判别式<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>，从而确定二次函数的图像与<i>x</i>轴的相交情况；如果有交点，则利用方程<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>=0解出交点的横坐标.
          </p>
          <p>
            第二步：画出二次函数<i>y</i>=<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>的简图.
          </p>
          <p>第三步：观察简图，写出不等式的解集.</p>
          <div class="bj">
            <examinations :cardList="questionData[54] ? questionData[54][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 048 -->
@@ -217,7 +2047,134 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <h3 id="c018">
            2.3.3 特殊类型一元二次不等式的解法<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>观察下列不等式：</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mn>1</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mn>3</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>＜</mo>
            <mn>0</mn>
            <mo>；</mo>
          </math>
          <p class="right">①</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mn>1</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mn>3</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>＞</mo>
            <mn>0</mn>
            <mo>；</mo>
          </math>
          <p class="right">②</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mn>1</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mn>3</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>≤</mo>
            <mn>0</mn>
            <mo>；</mo>
          </math>
          <p class="right">③</p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>+</mo>
              <mn>1</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">(</mo>
              <mi>x</mi>
              <mo>−</mo>
              <mn>3</mn>
              <mo data-mjx-texclass="CLOSE">)</mo>
            </mrow>
            <mo>≥</mo>
            <mn>0</mn>
            <mo>.</mo>
          </math>
          <p class="right">④</p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0059-5.jpg" /></p>
          <p class="img">图2-7</p>
          <p>
            以上四个不等式对应的二次函数为<i>y</i>=（<i>x</i>+1）（<i>x</i>-3），对应的一元二次方程为（<i>x</i>+1）（<i>x</i>-3）=0.其解为<i>x</i>1=-1，<i>x</i>2=3.二次函数<i>y</i>=（<i>x</i>+1）（<i>x</i>-3）的图像与<i>x</i>轴有两个交点（-1，0），（3，0）.
          </p>
          <p>二次函数<i>y</i>=（<i>x</i>+1）（<i>x</i>-3）的简图如图2-7所示.</p>
          <p>
            结合二次函数<i>y</i>=（<i>x</i>+1）（<i>x</i>-3）的简图，我们可以得到以下结论.
          </p>
          <p>
            （1）
            不等式（<i>x</i>+1）（<i>x</i>-3）＜0的解在方程（<i>x</i>+1）（<i>x</i>-3）=0的两解之间，解集为（-1，3）；
          </p>
          <p>
            （2）
            不等式（<i>x</i>+1）（<i>x</i>-3）＞0的解在方程（<i>x</i>+1）（<i>x</i>-3）=0的两解之外，解集为（-∞，-1）∪（3，+∞）；
          </p>
          <p>
            （3）
            不等式（<i>x</i>+1）（<i>x</i>-3）≤0的解在方程（<i>x</i>+1）（<i>x</i>-3）=0的两解之间，解集为［-1，3］；
          </p>
          <p>
            （4）
            不等式（<i>x</i>+1）（<i>x</i>-3）≥0的解在方程（<i>x</i>+1）（<i>x</i>-3）=0的两解之外，解集为（-∞，-1］∪［3，+∞）.
          </p>
          <p>
            一般地，一元二次方程（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）=0（其中<i>p</i>，<i>q</i>为实数，并且<i>p</i>＜<i>q</i>）有两个不相等的实数解<i>x</i>1=<i>p</i>，<i>x</i>2=<i>q</i>，二次函数<i>y</i>=（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）的简图如图2-8所示.
          </p>
          <p>
            观察二次函数<i>y</i>=（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）的简图，可知下列结论成立.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0059-6.jpg" /></p>
          <p class="img">图2-8</p>
          <p>
            （1）
            不等式（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）＜0的解集为（<i>p</i>，<i>q</i>）；
          </p>
          <p>
            （2）
            不等式（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）＞0的解集为（-∞，<i>p</i>）∪（<i>q</i>，+∞）；
          </p>
        </div>
      </div>
    </div>
    <!-- 049 -->
@@ -231,7 +2188,114 @@
            <p><span>049</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p>
            （3）
            不等式（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）≤0的解集为［<i>p</i>，<i>q</i>］；
          </p>
          <p>
            （4）
            不等式（<i>x</i>-<i>p</i>）（<i>x</i>-<i>q</i>）≥0的解集为（-∞，<i>p</i>］∪［<i>q</i>，+∞）.
          </p>
          <p>
            <span class="zt-ls"><b>例1</b></span>　解下列不等式.
          </p>
          <p class="p-btn" >
            <span>（1）（<i>x</i>+3）（<i>x</i>+1）＜0；</span>
            <span class="btn-box" @click="isShowAnswer14 = !isShowAnswer14">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer14" >
            <p >
              <span class="zt-ls"><b>解</b></span>（1）（<i>x</i>+3）（<i>x</i>+1）＜0，即［<i>x</i>-（-3）］［<i>x</i>-（-1）］＜0.
            </p>
            <p >所以不等式的解集为（-3，-1）.</p>
          </div>
          <p class="p-btn" >
            <span>（2）（6-<i>x</i>）（<i>x</i>+4）≤0.</span>
            <span class="btn-box" @click="isShowAnswer15 = !isShowAnswer15">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer15" >
            <p>
              <span class="zt-ls"><b>解</b></span>
            （2）
              由（6-<i>x</i>）（<i>x</i>+4）≤0得（<i>x</i>-6）（<i>x</i>+4）≥0，即
            </p>
            <p class="center">（<i>x</i>-6）［<i>x</i>-（-4）］≥0.</p>
            <p>所以不等式的解集为（-∞，-4］∪［6，+∞）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　解下列不等式.
            </span>
            <span class="btn-box" @click="openDialog(thinkTwo)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
                  d="M3771.2-14311.889a2.356,2.356,0,0,1-1.727-.626c-.027-.054-.053-.1-.079-.148l0-.007c-.123-.224-.2-.371-.076-.629a.869.869,0,0,1,.784-.471.205.205,0,0,1,.158.079.205.205,0,0,0,.158.079.187.187,0,0,0,.038.1.143.143,0,0,0,.117.05h.158a.573.573,0,0,0,.471.158,2.2,2.2,0,0,0,.916-.3l.023-.011a.572.572,0,0,1,.471-.158.575.575,0,0,1,.626.626.526.526,0,0,1,.036.409.664.664,0,0,1-.349.375A3.582,3.582,0,0,1,3771.2-14311.889Zm-1.885-1.723h-.155a.718.718,0,0,1-.784-.63.38.38,0,0,1-.021-.3.976.976,0,0,1,.492-.485l4.86-1.252a1.047,1.047,0,0,1,.784.626c.151.3-.128.61-.471.784l-4.705,1.256Zm-.155-1.885H3769a.716.716,0,0,1-.784-.626c-.149-.3.129-.611.471-.784l4.234-1.1v-.158l-.021.007a7.808,7.808,0,0,1-1.861.31,5.3,5.3,0,0,1-3.137-.942,5.789,5.789,0,0,1-2.666-4.076,6.421,6.421,0,0,1,1.256-5.018,7.038,7.038,0,0,1,2.194-1.568,7.848,7.848,0,0,1,2.666-.472,6.43,6.43,0,0,1,2.979.784,4.958,4.958,0,0,1,2.2,2.194,5.522,5.522,0,0,1,.313,5.177,13.113,13.113,0,0,1-1.256,1.882l-.313.313a2.156,2.156,0,0,0-.78,1.244l0,.012a1.731,1.731,0,0,1-1.727,1.723l-.313.158-3.292.939Zm1.256-6.271v1.256h1.41v-1.256Zm.784-4.234c.718,0,1.1.271,1.1.784a.925.925,0,0,1-.316.783l-.468.156a2.235,2.235,0,0,0-.63.471l-.012.024a2.2,2.2,0,0,0-.3.918v.155h1.1v-.155a1.2,1.2,0,0,1,.313-.629.543.543,0,0,0,.315-.153c.007,0,.315,0,.315-.16a1.226,1.226,0,0,0,.626-.626,2.277,2.277,0,0,0,.313-1.1,1.409,1.409,0,0,0-.626-1.252,2.337,2.337,0,0,0-1.569-.471,2.258,2.258,0,0,0-2.507,2.353l1.252.154A1.121,1.121,0,0,1,3771.2-14326Zm-6.51,9.645a.769.769,0,0,1-.549-.237.772.772,0,0,1-.235-.549.772.772,0,0,1,.235-.548l.939-.939a.781.781,0,0,1,.55-.234.772.772,0,0,1,.547.234.772.772,0,0,1,.238.549.772.772,0,0,1-.238.549l-.939.938A.769.769,0,0,1,3764.686-14316.356Zm13.174-.157a.774.774,0,0,1-.549-.234l-.943-.942a.678.678,0,0,1-.233-.47.678.678,0,0,1,.233-.47.774.774,0,0,1,.549-.234.774.774,0,0,1,.549.234l.942.939a.427.427,0,0,1,.228.324.74.74,0,0,1-.228.618A.774.774,0,0,1,3777.859-14316.514Zm2.9-6.351h-1.414c-.469-.158-.784-.474-.784-.784a.743.743,0,0,1,.784-.784h1.414a.743.743,0,0,1,.784.784A.743.743,0,0,1,3780.761-14322.864Zm-17.566-.158h-1.41c-.469-.157-.784-.473-.784-.784a.743.743,0,0,1,.784-.784h1.41a.743.743,0,0,1,.784.784A.743.743,0,0,1,3763.195-14323.022Zm13.861-5.723a.759.759,0,0,1-.529-.237.776.776,0,0,1-.235-.549.772.772,0,0,1,.235-.549l.939-.938a.44.44,0,0,1,.413-.238.759.759,0,0,1,.529.238.772.772,0,0,1,.235.549.772.772,0,0,1-.235.548l-.942.939A.435.435,0,0,1,3777.055-14328.745Zm-11.429,0a.776.776,0,0,1-.55-.237l-.939-1.1a.678.678,0,0,1-.235-.469.678.678,0,0,1,.235-.47.772.772,0,0,1,.549-.238.772.772,0,0,1,.549.238l.939,1.1a.675.675,0,0,1,.238.47.675.675,0,0,1-.238.47A.767.767,0,0,1,3765.626-14328.745Zm5.724-2.273a.743.743,0,0,1-.784-.785v-1.413c.157-.469.473-.784.784-.784a.743.743,0,0,1,.784.784v1.413A.743.743,0,0,1,3771.35-14331.019Z"
                  transform="translate(-3761 14334.001)" />
              </svg>
            </span>
          </p>
          <p class="p-btn" >
            <span>（1）（<i>x</i>+1）<sup>2</sup>≥4；</span>
            <span class="btn-box" @click="isShowAnswer16 = !isShowAnswer16">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer16" >
            <p>
              <span class="zt-ls"><b>解</b></span>（1）
              由（<i>x</i>+1）<sup>2</sup>≥4得（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，
            </p>
            <p>从而　　［（<i>x</i>+1）+2］［（<i>x</i>+1）-2］≥0，</p>
            <p>化简得（<i>x</i>+3）（<i>x</i>-1）≥0，</p>
            <p>即　　　［<i>x</i>-（-3）］（<i>x</i>-1）≥0，</p>
            <p>所以不等式的解集为（-∞，-3］∪［1，+∞）.</p>
          </div>
          <p class="p-btn" >
            <span>（2）（2<i>x</i>-3）<sup>2</sup>＜9.</span>
            <span class="btn-box" @click="isShowAnswer17 = !isShowAnswer17">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer17" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              （2）
              由（2<i>x</i>-3）<sup>2</sup>＜9得（2<i>x</i>-3）<sup>2</sup>-3<sup>2</sup>＜0，
            </p>
            <p>从而　　［（2<i>x</i>-3）+3］［（2<i>x</i>-3）-3］＜0，</p>
            <p>化简得　2<i>x</i>（2<i>x</i>-6）＜0，</p>
            <p>即　　　<i>x</i>（<i>x</i>-3）＜0，</p>
            <p>即（<i>x</i>-0）（<i>x</i>-3）＜0，</p>
            <p>所以不等式的解集为（0，3）.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <p>解下列一元二次不等式.</p>
            <examinations :cardList="questionData[56]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 050 -->
@@ -242,7 +2306,13 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <h3 id="c019">习题2.3<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[57]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 051 -->
@@ -257,7 +2327,142 @@
          </li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <h2 id="b010">
            2.4 含绝对值的不等式<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
          </h2>
          <h3 id="c020">
            2.4.1 含绝对值的不等式的基本解法<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/wttc.jpg" /></p>
          <p class="center"><b>商品房预售中的不等式知识</b></p>
          <p>
            商品房预售时，房地产开发企业将正在建设中的房屋预先出售给购房者，
            并在购房合同中约定所购买房屋的具体面积（称为“合同约定面积”）.房屋竣工后，
            根据现场实测的房屋面积被称为“产权登记面积”.为保护购房者权益，
            我国相关法律规定，
            预售房屋的购房合同中应当写明“合同约定面积”与“产权登记面积”发生误差时的处理方式.合同未作约定的，
            按以下原则处理：“（一） 面积误差比绝对值在3%以内（含3%） 的，
            根据‘产权登记面积’结算房价款；（二）
            面积误差比绝对值超出3%时，购房者有权退房.其中，
            面积误差比=（产权登记面积-合同约定面积）/合同约定面积×100%.”
          </p>
          <p>
            李先生购买预售房屋时， 合同约定面积为100 m<sup>2</sup>.房屋竣工后，
            产权登记面积在什么范围时， 李先生需要根据产权登记面积结算房价款？
            或者有权退房？
          </p>
          <div class="bk">
            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/zshg.jpg" />
              </p>
            </div>
            <p class="block">
              1.绝对值定义：数轴上表示数<i>a</i>的点与原点之间的距离叫作数<i>a</i>的绝对值，记作|<i>a</i>|.
            </p>
            <p class="block">
              2.一个正数的绝对值是它本身；一个负数的绝对值是它的相反数；0的绝对值是0，即
            </p>
            <p class="block">
              <math display="0">
                <mo stretchy="false">|</mo>
                <mi>a</mi>
                <mrow>
                  <mo stretchy="false">|</mo>
                </mrow>
                <mo>=</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>a</mi>
                        <mo>，</mo>
                        <mi>a</mi>
                        <mo>＞</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mn>0</mn>
                        <mo>，</mo>
                        <mi>a</mi>
                        <mo>=</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mo>−</mo>
                        <mi>a</mi>
                        <mo>，</mo>
                        <mi>a</mi>
                        <mo>＜</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>，也可以写成<math display="0">
                <mo stretchy="false">|</mo>
                <mi>a</mi>
                <mrow>
                  <mo stretchy="false">|</mo>
                </mrow>
                <mo>=</mo>
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">{</mo>
                  <mtable columnspacing="1em" rowspacing="4pt">
                    <mtr>
                      <mtd>
                        <mi>a</mi>
                        <mo>，</mo>
                        <mi>a</mi>
                        <mo>≥</mo>
                        <mn>0</mn>
                        <mo>，</mo>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                    <mtr>
                      <mtd>
                        <mo>−</mo>
                        <mi>a</mi>
                        <mo>，</mo>
                        <mi>a</mi>
                        <mo>＜</mo>
                        <mn>0</mn>
                      </mtd>
                      <mtd></mtd>
                      <mtd></mtd>
                    </mtr>
                  </mtable>
                  <mo data-mjx-texclass="CLOSE" fence="true" stretchy="true" symmetric="true"></mo>
                </mrow>
              </math>.
            </p>
            <p class="block">
              3.设<i>a</i>＞0，数轴上与原点的距离是<i>a</i>的点有两个，它们分别在原点两侧，分别是-<i>a</i>和<i>a</i>，如图2-9所示.
            </p>
            <p class="center">
              <img class="img-c" alt="" src="../../assets/images/0062-3.jpg" />
            </p>
            <p class="img">图2-9</p>
          </div>
        </div>
      </div>
    </div>
    <!-- 052 -->
@@ -268,7 +2473,76 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            假设产权登记面积为<i>x</i>（m<sup>2</sup>），上述问题可用一个含有绝对值的不等式表示.
          </p>
          <math display="block">
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">|</mo>
              <mfrac>
                <mrow>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>100</mn>
                </mrow>
                <mn>100</mn>
              </mfrac>
              <mo data-mjx-texclass="CLOSE">|</mo>
            </mrow>
            <mo>≤</mo>
            <mn>3%</mn>
            <mo>，或</mo>
            <mrow data-mjx-texclass="INNER">
              <mo data-mjx-texclass="OPEN">|</mo>
              <mfrac>
                <mrow>
                  <mi>x</mi>
                  <mo>−</mo>
                  <mn>100</mn>
                </mrow>
                <mn>100</mn>
              </mfrac>
              <mo data-mjx-texclass="CLOSE">|</mo>
            </mrow>
            <mo>＞</mo>
            <mn>3%</mn>
            <mo>，</mo>
          </math>
          <p>可化为　|<i>x</i>-100|≤3，或|<i>x</i>-100|＞3.</p>
          <p>如果我们能解出这两个不等式，就能回答上述问题.</p>
          <p>那么，如何解这种含有绝对值的不等式呢？我们先从简单的情形开始分析.</p>
          <p>
            设<i>a</i>＞0，由绝对值的意义可知，含有绝对值的方程|<i>x</i>|=<i>a</i>的解是<i>x</i>=<i>a</i>或<i>x</i>=-<i>a</i>.那么，含有绝对值的不等式（如|<i>x</i>|≥<i>a</i>，|<i>x</i>|＞<i>a</i>，|<i>x</i>|≤<i>a</i>，|<i>x</i>|＜<i>a</i>等）
            怎么解呢？下面以不等式|<i>x</i>|≤<i>a</i>（<i>a</i>＞0）
            和|<i>x</i>|＞<i>a</i>（<i>a</i>＞0）为例进行分析.
          </p>
          <p>
            由绝对值的几何意义，|<i>x</i>|表示实数<i>x</i>对应的点与原点之间的距离.因此，不等式|<i>x</i>|≤<i>a</i>（<i>a</i>＞0）
            表示数轴上到原点的距离不大于<i>a</i>的点的集合.在数轴上，满足|<i>x</i>|≤<i>a</i>（<i>a</i>＞0）
            的实数<i>x</i>对应的点如图2-10所示.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0063-2.jpg" /></p>
          <p class="img">图2-10</p>
          <p>
            所以不等式|<i>x</i>|≤<i>a</i>（<i>a</i>＞0）
            的解集是{<i>x</i>|-<i>a</i>≤<i>x</i>≤<i>a</i>}，用区间表示为［-<i>a</i>，<i>a</i>］.
          </p>
          <p>
            同理，不等式|<i>x</i>|＞<i>a</i>（<i>a</i>＞0）
            表示数轴上到原点的距离大于<i>a</i>的点的集合.在数轴上，满足|<i>x</i>|＞<i>a</i>（<i>a</i>＞0）的实数<i>x</i>对应的点如图2-11所示.
          </p>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0063-3.jpg" /></p>
          <p class="img">图2-11</p>
          <p>
            所以不等式|<i>x</i>|＞<i>a</i>（<i>a</i>＞0） 的解集是
            {<i>x</i>|<i>x</i>＜-<i>a</i>或<i>x</i>＞<i>a</i>}，用区间表示为（-∞，-<i>a</i>）∪（<i>a</i>，+∞）.
          </p>
          <p>由此，可以得到表2-6.</p>
          <p class="img">表2-6</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0063-4.jpg" /></p>
        </div>
      </div>
    </div>
    <!-- 053 -->
@@ -282,7 +2556,127 @@
            <p><span>053</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="p-btn" >
            <span>
              <b>例</b> 解不等式|2<i>x</i>|＜5.
            </span>
            <span class="btn-box" @click="isShowAnswer18 = !isShowAnswer18">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer18" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|2<i>x</i>|＜5得-5＜2<i>x</i>＜5，
            </p>
            <p>
              即　<math display="0">
                <mo>−</mo>
                <mfrac>
                  <mn>5</mn>
                  <mn>2</mn>
                </mfrac>
                <mo>＜</mo>
                <mi>x</mi>
                <mo>＜</mo>
                <mfrac>
                  <mn>5</mn>
                  <mn>2</mn>
                </mfrac>
              </math>.
            </p>
            <p>
              所以不等式的解集是<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mo>−</mo>
                  <mfrac>
                    <mn>5</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo>，</mo>
                  <mfrac>
                    <mn>5</mn>
                    <mn>2</mn>
                  </mfrac>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>.
            </p>
          </div>
          <div class="bk-hzjl">
            <div class="bj1-hzjl">
              <p class="left">
                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
              </p>
            </div>
            <examinations :cardList="questionData[60] ? questionData[60][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations :cardList="questionData[60] ? questionData[60][2] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h3 id="c021">
            2.4.2
            |<i>ax</i>+<i>b</i>|＜<i>c</i>和|<i>ax</i>+<i>b</i>|＞<i>c</i>（<i>c</i>＞0）的解法<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/fxlj.jpg" /></p>
          <p>
            求解此类不等式时，可以将<i>ax</i>+<i>b</i>看作一个整体，再利用含绝对值不等式的基本解法，去掉绝对值，然后进行求解.
          </p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　解不等式|2<i>x</i>-1|＜5.
            </span>
            <span class="btn-box" @click="isShowAnswer19 = !isShowAnswer19">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer19" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|2<i>x</i>-1|＜5得-5＜2<i>x</i>-1＜5，
            </p>
            <p>即　-4＜2<i>x</i>＜6，</p>
            <p>　　-2＜<i>x</i>＜3.</p>
            <p>所以不等式的解集是（-2，3）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例2</b></span>　解不等式|1-2<i>x</i>|＜3.
            </span>
            <span class="btn-box" @click="isShowAnswer20 = !isShowAnswer20">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer20" >
            <p>
              <span class="zt-ls"><b>解</b></span> 因为|1-2<i>x</i>|=|2<i>x</i>-1|，
            </p>
            <p>所以由|1-2<i>x</i>|＜3得|2<i>x</i>-1|＜3.</p>
            <p>由|2<i>x</i>-1|＜3得-3＜2<i>x</i>-1＜3，</p>
            <p>即　-2＜2<i>x</i>＜4，</p>
            <p>　　-1＜<i>x</i>＜2.</p>
            <p>所以不等式的解集是（-1，2）.</p>
          </div>
        </div>
      </div>
    </div>
    <!-- 054 -->
@@ -293,8 +2687,63 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例3</b></span>　解不等式|<i>x</i>+3|≥2.
            </span>
            <span class="btn-box" @click="isShowAnswer21 = !isShowAnswer21">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer21" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|<i>x</i>+3|≥2得<i>x</i>+3≤-2或<i>x</i>+3≥2，
            </p>
            <p>即　<i>x</i>≤-5或<i>x</i>≥-1.</p>
            <p>所以不等式的解集是（-∞，-5］∪［-1，+∞）.</p>
            <p>
              现在我们回到本节开始的问题，解不等式|<i>x</i>-100|≤3得97≤<i>x</i>≤103，解不等式|<i>x</i>-100|＞3得<i>x</i>＞103或<i>x</i>＜97.如果产权登记面积在97
              m<sup>2</sup>和103 m<sup>2</sup>之间（包含97 m<sup>2</sup>和103
              m<sup>2</sup>）
              时，李先生按照产权登记面积结算房款；如果产权登记面积小于97
              m<sup>2</sup>或大于103 m<sup>2</sup>时，李先生有权退房.
            </p>
          </div>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例4</b></span>　解不等式|3<i>x</i>-（<i>x</i>-2）|≤2.
            </span>
            <span class="btn-box" @click="isShowAnswer22 = !isShowAnswer22">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer22">
            <p>
              <span class="zt-ls"><b>解</b></span>
              由|3<i>x</i>-（<i>x</i>-2）|≤2得|3<i>x</i>-<i>x</i>+2|≤2，
            </p>
            <p>即　　|2<i>x</i>+2|≤2，</p>
            <p>从而　-2≤2<i>x</i>+2≤2，</p>
            <p>　　　-4≤2<i>x</i>≤0，</p>
            <p>　　　-2≤<i>x</i>≤0.</p>
            <p>所以不等式的解集是［-2，0］.</p>
          </div>
          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
          <div class="bj">
            <examinations :cardList="questionData[61]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 055 -->
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            <p><span>055</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <h3 id="c022">习题2.4<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[62]" :hideCollect="true" sourceType="json" inputBc="#d3edfa"
              v-if="questionData"></examinations>
          </div>
          <h2 id="b011">
            2.5 不等式的应用<span class="fontsz1">＞＞＞＞＞＞＞＞</span>
          </h2>
          <h3 id="c023">
            2.5.1 不等式的简单应用<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="center"><img class="img-c" alt="" src="../../assets/images/0066-11.jpg" /></p>
          <p class="img">图2-12</p>
          <p class="p-btn" >
            <span>
              <span class="zt-ls"><b>例1</b></span>　用篱笆在墙边围一块矩形小花坛，其中一边靠墙（如图2-12所示），篱笆总长为8m.若小花坛的面积不小于6
              m<sup>2</sup>，则小花坛垂直于墙的一边的长度范围是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer23 = !isShowAnswer23">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p v-if="isShowAnswer23" >
            <span class="zt-ls"><b>解</b></span>
            设小花坛垂直于墙的一边的长度为<i>x</i>（m），则与墙平行的一边的长度为（8-2<i>x</i>）m.考虑到实际情况，有<i>x</i>＞0，并且8-2<i>x</i>＞0，所以<i>x</i>满足0＜<i>x</i>＜4.
          </p>
        </div>
      </div>
    </div>
    <!-- 056 -->
@@ -319,7 +2799,94 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <div v-if="isShowAnswer23">
            <p>设小花坛的面积为<i>S</i>（m<sup>2</sup>），则</p>
            <p class="center"><i>S</i>=<i>x</i>（8-2<i>x</i>），</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0067-1.jpg" /></p>
            <p class="img">图2-13</p>
            <p>整理得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>.</p>
            <p>
              由题意得 <i>S</i>=-2<i>x</i><sup>2</sup>+8<i>x</i>≥6，即<i>x</i><sup>2</sup>-4<i>x</i>+3≤0.
            </p>
            <p>
              画出二次函数<i>y</i>=<i>x</i><sup>2</sup>-4<i>x</i>+3的简图（如图2-13所示）.
            </p>
            <p>由图像得不等式的解为{<i>x</i>|1≤<i>x</i>≤3}.</p>
            <p>结合0＜<i>x</i>＜4，得</p>
            <p class="center">
              {<i>x</i>|0＜<i>x</i>＜4}∩{<i>x</i>|1≤<i>x</i>≤3}={<i>x</i>|1≤<i>x</i>≤3}.
            </p>
            <p>所以小花坛垂直于墙的一边的长度在1m至3m之间（含1m和3m）.</p>
          </div>
          <p class="p-btn" >
            <span>
              <span
              class="zt-ls"><b>例2</b></span>　某网店销售一种电动玩具，成本为10元/个.平时按单价20元销售，日平均销售量为100个.为进一步提升业绩，该网店决定在“双11”期间举办降价促销活动.根据以往的统计，如果该电动玩具的单价每降低0.5元，日平均销售量就会大约增加10个.为了使促销活动期间日平均利润不低于平时，应如何确定降价的范围？
            </span>
            <span class="btn-box" @click="isShowAnswer24 = !isShowAnswer24">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
            <span class="btn-box" @click="openDialog(thinkThree)">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.545" height="18.112" viewBox="0 0 20.545 22.112">
                <path class="a"
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                  transform="translate(-3761 14334.001)" />
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            <div class="bj1">
              <p class="left">
                <img class="img-gn1" alt="" src="../../assets/images/tbts.jpg" />
              </p>
            </div>
            <p class="block">
              由例1和例2可知，在解决与一元二次不等式有关的实际问题时，不仅要解一元二次不等式，而且要考虑实际背景对未知数的限制.在例1中，实际背景对未知数的限制是0＜<i>x</i>＜4；在例2中，实际背景对未知数的限制是0＜<i>x</i>＜10.
            </p>
          </div>
          <div v-if="isShowAnswer24">
            <p>
              <span class="zt-ls"><b>解</b></span>
              假设降价<i>x</i>元.考虑到实际情况，价格的降幅应小于10元，即保证销售价高于成本价，所以要求<i>x</i>＞0并且<i>x</i>＜10，即0＜<i>x</i>＜10.
            </p>
            <p>平时的日平均利润为（20-10）×100=1 000（元）.</p>
            <p>
              降价<i>x</i>元后，销售单价为（20-<i>x</i>）元，单个玩具的利润为（20-<i>x</i>）-10=（10-<i>x</i>）元，日平均销售量为<math display="0">
                <mrow data-mjx-texclass="INNER">
                  <mo data-mjx-texclass="OPEN">(</mo>
                  <mn>100</mn>
                  <mo>+</mo>
                  <mfrac>
                    <mn>10</mn>
                    <mn>0.5</mn>
                  </mfrac>
                  <mi>x</mi>
                  <mo data-mjx-texclass="CLOSE">)</mo>
                </mrow>
              </math>个.因此，降价<i>x</i>元后的日平均利润为（10-<i>x</i>）（100+20<i>x</i>）元.
            </p>
            <p>由题意得（10-<i>x</i>）（100+20<i>x</i>）≥1 000.</p>
            <p>化简得<i>x</i><sup>2</sup>-5<i>x</i>≤0，即<i>x</i>（<i>x</i>-5）≤0.</p>
            <p>所以不等式的解集为 {<i>x</i>|0≤<i>x</i>≤5}.</p>
            <p>
              由于0＜<i>x</i>＜10，所以<i>x</i>的范围是{<i>x</i>|0＜<i>x</i>＜10}∩{<i>x</i>|0≤<i>x</i>≤5}，即{<i>x</i>|0＜<i>x</i>≤5}.所以降价的范围应在0至5元之间（含5元，不含0元），即单价定在15元至20元之间（含15元，不含20元），便能满足要求.
            </p>
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                <img class="img-gn2" alt="" src="../../assets/images/hzjl.jpg" />
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            <p><span>057</span></p>
          </li>
        </ul>
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          <p class="left"><img class="img-gn" alt="" src="../../assets/images/stlx.jpg" /></p>
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            <examinations :cardList="questionData[64]" :hideCollect="true" sourceType="json" v-if="questionData">
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          <h3 id="c024">
            2.5.2 不等式与复杂实际问题<span class="fontsz2">＞＞＞</span>
          </h3>
          <p class="p-btn" >
            <span>
              <span
                class="zt-ls"><b>例1</b></span>　我国交通法规对小型汽车驾驶员的年龄限制如下：最低年龄18周岁，最高年龄70周岁.已有研究表明，小型汽车驾驶员对红绿灯变化的反应时间<i>y</i>（ms）
              与驾驶员年龄<i>x</i>（周岁）
              的关系为<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22，其中18≤<i>x</i>≤70.问：反应时间超过24.5ms的驾驶员所处的年龄范围是多少？
            </span>
            <span class="btn-box" @click="isShowAnswer25 = !isShowAnswer25">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
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                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <div v-if="isShowAnswer25" >
            <p>
              <span class="zt-ls"><b>解</b></span> 由题意得，<i>y</i>=0.005<i>x</i><sup>2</sup>-0.2<i>x</i>+22＞24.5，即
            </p>
            <p>　　　　　0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0.</p>
            <p>化简得 <i>x</i><sup>2</sup>-40<i>x</i>-500＞0.</p>
            <p class="center"><img class="img-c" alt="" src="../../assets/images/0068-2.jpg" /></p>
            <p class="img">图2-14</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-40）<sup>2</sup>-4×1×（-500）=3
              600＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>-500的图像开口向上，并且与<i>x</i>轴有两个交点.其简图如图2-14所示.
            </p>
            <p>
              由图像可知，不等式<i>x</i><sup>2</sup>-40<i>x</i>-500＞0的解集为（-∞，-10）∪（50，+∞），这也是不等式0.005<i>x</i><sup>2</sup>-0.2<i>x</i>-2.5＞0的解集.
            </p>
            <p>
              考虑到18≤<i>x</i>≤70，所以<i>x</i>的范围是（50，70］，即反应时间超过24.5
              <i>ms</i>
              的驾驶员所处的年龄范围在50岁至70岁之间（不包含50岁，包含70岁）.
            </p>
          </div>

        <div class="padding-116"></div>
          <p>
            <span class="zt-ls"><b>例2</b></span>　身体质量指数（Body Mass
            Index，BMI）是衡量人体胖瘦程度的一个常用标准，计算公式为<math display="0">
              <mi>B</mi>
              <mi>M</mi>
              <mi>I</mi>
              <mo>=</mo>
              <mfrac>
                <mrow>
                  <mo>体重</mo>
                </mrow>
                <msup>
                  <mrow data-mjx-texclass="INNER">
                    <mo data-mjx-texclass="OPEN">(</mo>
                    <mo>身高</mo>
                    <mo data-mjx-texclass="CLOSE">)</mo>
                  </mrow>
                  <mrow>
                    <mn>2</mn>
                  </mrow>
                </msup>
              </mfrac>
            </math>（BMI单位：kg/m<sup>2</sup>）.一项研究指出，中职学生身体质量指数与身体素质之间存在一定的关系.研究中使用身体素质指标来衡量学
          </p>
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          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <p>
            生的身体素质，该指标是指学生参加50m跑，立定跳远，力量（男生引体向上、女生1分钟仰卧起坐），耐力跑（男生1
            000m跑、女生800m跑），坐位体前屈等项目的成绩总和.身体素质指标为正数说明身体素质较好.上述研究发现，身体素质指标（<i>y</i>）与BMI（<i>x</i>）
            之间的关系如表2-7所示.
          </p>
          <p class="p-btn" >
            问：身体素质较好的男生和女生，其BMI的范围分别是多少？
            <span class="btn-box" @click="isShowAnswer26 = !isShowAnswer26">
              <svg xmlns="http://www.w3.org/2000/svg" width="16.501" height="16.501" viewBox="0 0 20.501 20.501">
                <path class="a"
                  d="M3344.717-15308.5H3337.4a10.186,10.186,0,0,1-7.25-3,10.185,10.185,0,0,1-3-7.25A10.262,10.262,0,0,1,3337.4-15329a10.26,10.26,0,0,1,10.249,10.248,10.129,10.129,0,0,1-2.2,6.341v3.177A.734.734,0,0,1,3344.717-15308.5Zm-9.606-7.29h4.493l.527,1.419c.071.182.156.386.254.608a2.428,2.428,0,0,0,.273.512.986.986,0,0,0,.315.262.971.971,0,0,0,.454.1,1.05,1.05,0,0,0,.773-.327,1.025,1.025,0,0,0,.319-.723,3.3,3.3,0,0,0-.277-1.051l-.062-.161-2.889-7.313c-.119-.321-.228-.607-.335-.873a2.972,2.972,0,0,0-.323-.616,1.56,1.56,0,0,0-.5-.469,1.552,1.552,0,0,0-.781-.181,1.535,1.535,0,0,0-.773.181,1.475,1.475,0,0,0-.5.477,3.674,3.674,0,0,0-.362.739l-.239.627-.054.135-2.824,7.355c-.095.229-.179.46-.25.688a1.529,1.529,0,0,0-.073.477.978.978,0,0,0,.323.72,1.039,1.039,0,0,0,.746.315.838.838,0,0,0,.716-.3,4.676,4.676,0,0,0,.466-.985l.062-.165.527-1.449Zm3.747-1.5h-3.293l1.812-5.124,1.481,5.123Z"
                  transform="translate(-3327.144 15329)" />
              </svg>
            </span>
          </p>
          <p class="img">表2-7</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0069-1.jpg" /></p>
          <div v-if="isShowAnswer26" >
            <p>
              <span class="zt-ls"><b>解</b></span>
              先考虑男生的情况.由题意得，<i>y</i>=-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0，即
            </p>
            <p class="center">0.05<i>x</i><sup>2</sup>-2<i>x</i>+19.2＜0.</p>
            <p>化简得　<i>x</i><sup>2</sup>-40<i>x</i>+384＜0.</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=40<sup>2</sup>-4×1×384=64＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-40<i>x</i>+384的图像开口向上，与<i>x</i>轴有两个交点.
            </p>
            <p>
              所以不等式<i>x</i><sup>2</sup>-40<i>x</i>+384＜0的解集为（16，24），这也是不等式-0.05<i>x</i><sup>2</sup>+2<i>x</i>-19.2＞0的解集.
            </p>
            <p>
              再考虑女生的情况.由题意得，<i>y</i>=-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0，即
            </p>
            <p class="center">0.01<i>x</i><sup>2</sup>-0.39<i>x</i>+3.68＜0.</p>
            <p>化简得　<i>x</i><sup>2</sup>-39<i>x</i>+368＜0.</p>
            <p>
              考查二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368，<i>a</i>=1＞0，<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>=（-39）<sup>2</sup>-4×1×368=49＞0，所以二次函数<i>y</i>=<i>x</i><sup>2</sup>-39<i>x</i>+368的图像开口向上，与<i>x</i>轴有两个交点.
            </p>
            <p>
              所以不等式<i>x</i><sup>2</sup>-39<i>x</i>+368＜0的解集为（16，23），这也是不等式-0.01<i>x</i><sup>2</sup>+0.39<i>x</i>-3.68＞0的解集.
            </p>
            <p>
              因此，身体素质较好的男生BMI 的范围是（16，24），身体素质较好的女生BMI
              的范围是（16，23）.
            </p>
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@@ -357,22 +3048,29 @@
            <p>第二单元 不等式</p>
          </li>
          <li>
            <p><span>059</span></p>
            <p><span>059-060</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p class="left">
            <img class="img-gn" alt="" src="../../assets/images/stlx.jpg" />
          </p>
          <div class="bj">
            <examinations :cardList="questionData[66] ? questionData[66][1] : []" :hideCollect="true" sourceType="json"
              inputBc="#d3edfa" v-if="questionData"></examinations>
          </div>
          <h3 id="c025">习题2.5<span class="fontsz2">＞＞＞</span></h3>
          <div class="bj">
            <examinations :cardList="questionData[66] ? questionData[66][2] : []" :hideCollect="true" sourceType="json"
              v-if="questionData">
            </examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 060 -->
    <div class="page-box" page="67">
      <div v-if="showPageList.indexOf(67) > -1">
        <ul class="page-header-odd fl al-end">
          <li>060</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
      </div>
    <div class="page-box hidePage" page="67">

    </div>
    <!-- 061 -->
    <div class="page-box" page="68">
@@ -385,7 +3083,117 @@
            <p><span>061</span></p>
          </li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <h2 id="b012">数学园地<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <p>
            本单元中，我们学习了不等式的一些性质，以及如何解一元二次不等式和含绝对值的不等式.实际上，数学领域中还有很多不等式，也被用来解决生产生活中的实际问题.尤其是微积分体系建立以前，不等式是计算最大值和最小值问题的最佳工具.下面我们介绍一些著名的不等式.
          </p>
          <p>
            填写表2-8，并观察<math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mrow>
                <mn>2</mn>
              </mfrac>
            </math>，<math display="0">
              <msqrt>
                <mi>a</mi>
                <mi>b</mi>
              </msqrt>
            </math>，<math display="0">
              <mfrac>
                <mn>2</mn>
                <mrow>
                  <mfrac>
                    <mn>1</mn>
                    <mi>a</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>b</mi>
                  </mfrac>
                </mrow>
              </mfrac>
            </math>这三个数的大小关系.
          </p>
          <p class="img">表2-8</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0072-4.jpg" /></p>
          <p>
            填写表2-9，并观察<math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mn>3</mn>
              </mfrac>
            </math>，<math display="0">
              <mroot>
                <mrow>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mrow>
                <mn>3</mn>
              </mroot>
            </math>，<math display="0">
              <mfrac>
                <mn>3</mn>
                <mrow>
                  <mfrac>
                    <mn>1</mn>
                    <mi>a</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>b</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>b</mi>
                  </mfrac>
                </mrow>
              </mfrac>
            </math>这三个数的大小关系.
          </p>
          <p class="img">表2-9</p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0072-8.jpg" /></p>
          <p>通过填写和观察上面两个表格，你有什么发现和猜想？</p>
          <p>实际上，若<i>a</i>，<i>b</i>，<i>c</i>均为正数，则可给出如下定义.</p>
          <p>
            （1）
            <math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                </mrow>
                <mn>2</mn>
              </mfrac>
            </math>叫作<i>a</i>，<i>b</i>两数的算术平均数，<math display="0">
              <mfrac>
                <mrow>
                  <mi>a</mi>
                  <mo>+</mo>
                  <mi>b</mi>
                  <mo>+</mo>
                  <mi>c</mi>
                </mrow>
                <mn>3</mn>
              </mfrac>
            </math>叫作<i>a</i>，<i>b</i>，<i>c</i>三数的算术平均数；
          </p>
        </div>
      </div>
    </div>
    <!-- 062 -->
@@ -396,7 +3204,264 @@
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116"></div>
        <div class="padding-116">
          <p>
            （2）
            <math display="0">
              <msqrt>
                <mi>a</mi>
                <mi>b</mi>
              </msqrt>
            </math>叫作<i>a</i>，<i>b</i>两数的几何平均数，<math display="0">
              <mroot>
                <mrow>
                  <mi>a</mi>
                  <mi>b</mi>
                  <mi>c</mi>
                </mrow>
                <mn>3</mn>
              </mroot>
            </math>叫作<i>a</i>，<i>b</i>，<i>c</i>三数的几何平均数；
          </p>
          <p>
            （3）
            <math display="0">
              <mfrac>
                <mn>2</mn>
                <mrow>
                  <mfrac>
                    <mn>1</mn>
                    <mi>a</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>b</mi>
                  </mfrac>
                </mrow>
              </mfrac>
            </math>叫作<i>a</i>，<i>b</i>两数的调和平均数，<math display="0">
              <mfrac>
                <mn>3</mn>
                <mrow>
                  <mfrac>
                    <mn>1</mn>
                    <mi>a</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>b</mi>
                  </mfrac>
                  <mo>+</mo>
                  <mfrac>
                    <mn>1</mn>
                    <mi>c</mi>
                  </mfrac>
                </mrow>
              </mfrac>
            </math>叫作<i>a</i>，<i>b</i>，<i>c</i>三数的调和平均数.
          </p>
          <p>观察上面两个表格，可以发现</p>
          <math display="block">
            <mfrac>
              <mrow>
                <mi>a</mi>
                <mo>+</mo>
                <mi>b</mi>
              </mrow>
              <mn>2</mn>
            </mfrac>
            <mo>⩾</mo>
            <msqrt>
              <mi>a</mi>
              <mi>b</mi>
            </msqrt>
            <mo>⩾</mo>
            <mfrac>
              <mn>2</mn>
              <mrow>
                <mfrac>
                  <mn>1</mn>
                  <mi>a</mi>
                </mfrac>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>b</mi>
                </mfrac>
              </mrow>
            </mfrac>
            <mo>,</mo>
            <mfrac>
              <mrow>
                <mi>a</mi>
                <mo>+</mo>
                <mi>b</mi>
                <mo>+</mo>
                <mi>c</mi>
              </mrow>
              <mn>3</mn>
            </mfrac>
            <mo>⩾</mo>
            <mroot>
              <mrow>
                <mi>a</mi>
                <mi>b</mi>
                <mi>c</mi>
              </mrow>
              <mn>3</mn>
            </mroot>
            <mo>⩾</mo>
            <mfrac>
              <mn>3</mn>
              <mrow>
                <mfrac>
                  <mn>1</mn>
                  <mi>a</mi>
                </mfrac>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>b</mi>
                </mfrac>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <mi>c</mi>
                </mfrac>
              </mrow>
            </mfrac>
            <mo>.</mo>
          </math>
          <p>
            大胆地想一想，对于<i>n</i>个正数的算术平均数、几何平均数、调和平均数，怎样用符号表示？它们的大小关系能确定吗？
          </p>
          <p>
            一般地，若<i>a</i>1，<i>a</i>2，<i>a</i>3，…，<i>an</i>为<i>n</i>个正数，则有
          </p>
          <math display="block">
            <mfrac>
              <mrow>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>1</mn>
                  </mrow>
                </msub>
                <mo>+</mo>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>2</mn>
                  </mrow>
                </msub>
                <mo>+</mo>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>3</mn>
                  </mrow>
                </msub>
                <mo>+</mo>
                <mo>⋯</mo>
                <mo>+</mo>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mi>n</mi>
                  </mrow>
                </msub>
              </mrow>
              <mi>n</mi>
            </mfrac>
            <mo>⩾</mo>
            <mroot>
              <mrow>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>1</mn>
                  </mrow>
                </msub>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>2</mn>
                  </mrow>
                </msub>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mn>3</mn>
                  </mrow>
                </msub>
                <mo>⋯</mo>
                <msub>
                  <mi>a</mi>
                  <mrow>
                    <mi>n</mi>
                  </mrow>
                </msub>
              </mrow>
              <mi>n</mi>
            </mroot>
            <mo>⩾</mo>
            <mfrac>
              <mi>n</mi>
              <mrow>
                <mfrac>
                  <mn>1</mn>
                  <msub>
                    <mi>a</mi>
                    <mrow>
                      <mn>1</mn>
                    </mrow>
                  </msub>
                </mfrac>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <msub>
                    <mi>a</mi>
                    <mrow>
                      <mn>2</mn>
                    </mrow>
                  </msub>
                </mfrac>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <msub>
                    <mi>a</mi>
                    <mrow>
                      <mn>3</mn>
                    </mrow>
                  </msub>
                </mfrac>
                <mo>+</mo>
                <mo>⋯</mo>
                <mo>+</mo>
                <mfrac>
                  <mn>1</mn>
                  <msub>
                    <mi>a</mi>
                    <mrow>
                      <mi>n</mi>
                    </mrow>
                  </msub>
                </mfrac>
              </mrow>
            </mfrac>
            <mo>.</mo>
          </math>
          <p>
            其中，当<i>a</i><sub>1</sub>=<i>a</i><sub>1</sub>=<i>a</i><sub>1</sub>=…=<i>an</i>时，等号成立.
          </p>
          <p>
            随着学习的进一步深入，我们就能够证明数学史上这个著名的不等式，并且知道它的广泛应用.
          </p>
        </div>
      </div>
    </div>
    <!-- 063 -->
@@ -410,8 +3475,46 @@
            <p><span>063</span></p>
          </li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <h2 id="b013">单元小结<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <p class="bj2"><b>学习导图</b></p>
          <p class="center"><img class="img-a" alt="" src="../../assets/images/0074-1.jpg" /></p>
          <p class="bj2"><b>学习指导</b></p>
          <p>1.不等式的基本性质.</p>
          <p>（1） 比较数（式）的大小常用“作差比较法”.</p>
          <p>（2） 运用不等式的性质时，要注意验证条件是否都满足.</p>
          <p>2.区间.</p>
          <p>
            区间是集合的一种表示形式，主要包括开区间、闭区间、左开右闭区间和右开左闭区间.
          </p>
          <p>3.一元二次不等式.</p>
          <p>
            （1） 将一元二次不等式统一化成<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0（≥0）
            或<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0（≤0）
            的形式.
          </p>
          <p>
            （2） 若<i>a</i>＞0，此时二次函数的图像开口向上，计算判别式<i>Δ</i>=<i>b</i><sup>2</sup>-4<i>ac</i>.
          </p>
          <p>
            ①当<i>Δ</i>＞0时，二次函数的图像与<i>x</i>轴有两个不同的交点（<i>x</i><sub>1</sub>，0），（<i>x</i><sub>2</sub>，0）（<i>x</i><sub>1</sub>＜<i>x</i><sub>2</sub>）.画出函数简图，可得如下结论.
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0的解集为（-∞，<i>x</i><sub>1</sub>）∪（<i>x</i><sub>2</sub>，+∞）；
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≥0的解集为（-∞，<i>x</i><sub>1</sub>］∪［<i>x</i><sub>2</sub>，+∞）；
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0的解集为（<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>）；
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≤0的解集为 ［<i>x</i><sub>1</sub>，<i>x</i><sub>2</sub>］.
          </p>
          <p>
            ②当<i>Δ</i>=0时，二次函数的图像与<i>x</i>轴只有一个交点（<i>x</i><sub>0</sub>，0）.画出函数简图，可得如下结论.
          </p>
        </div>
      </div>
    </div>
    <!-- 064 -->
@@ -423,58 +3526,219 @@
          <li>上册</li>
        </ul>

        <div class="padding-116"></div>
        <div class="padding-116">
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0的解集为（-∞，<i>x</i><sub>0</sub>）∪（<i>x</i><sub>0</sub>，+∞）；
          </p>
          <p><i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≥0的解集为<b>R</b>；</p>
          <p><i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0的解集为 ∅；</p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≤0的解集为 {<i>x</i>|<i>x</i>=<i>x</i><sub>0</sub>}.
          </p>
          <p>
            ③当<i>Δ</i>＜0时，二次函数的图像与<i>x</i>轴没有交点.画出函数简图，可得如下结论.
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＞0和<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≥0的解集均为<b>R</b>；
          </p>
          <p>
            <i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>＜0和<i>ax</i><sup>2</sup>+<i>bx</i>+<i>c</i>≤0的解集均为 ∅.
          </p>
          <p>
            （3）
            若<i>a</i>＜0，则可以转化为-<i>ax</i><sup>2</sup>-<i>bx</i>-<i>c</i>＞0（≥0）或-<i>ax</i><sup>2</sup>-<i>bx</i>-<i>c</i>＜0（≤0）的情形，然后再按步骤（2）
            的方法进行求解.
          </p>
          <p>4.含绝对值的不等式.</p>
          <p>
            （1）
            不等式｜<i>x</i>｜≤<i>a</i>（<i>a</i>＞0）的解集是{<i>x</i>｜-<i>a</i>≤<i>x</i>≤<i>a</i>}，用区间表示为［-<i>a</i>，<i>a</i>］.
          </p>
          <p>
            （2）
            不等式｜<i>x</i>｜＞<i>a</i>（<i>a</i>＞0）的解集是{<i>x</i>｜<i>x</i>＜-<i>a</i>或<i>x</i>＞<i>a</i>}，用区间表示为（-∞，-<i>a</i>）∪（<i>a</i>，+∞）.
          </p>
          <p>
            （3）
            求解形如｜<i>ax</i>+<i>b</i>｜＜<i>c</i>和｜<i>ax</i>+<i>b</i>｜＞<i>c</i>（<i>c</i>＞0）的不等式时，可以将<i>ax</i>+<i>b</i>看作一个整体，
            再利用含绝对值不等式的基本解法， 去掉绝对值， 然后进行求解.
          </p>
          <p>5.不等式的应用.</p>
          <p>
            （1）
            在解决问题的过程中体验如何使用二次函数的图像直观地得出一元二次不等式的解集，学会利用数形结合的思想方法解决问题.
          </p>
          <p>（2） 应用一元二次不等式解决实际问题时，要注意未知量的实际意义.</p>
        </div>
      </div>
    </div>
    <!-- 065 -->
    <div class="page-box" page="72">
      <div v-if="showPageList.indexOf(72) > -1">

        <ul class="page-header-box">
          <li>
            <p>第二单元 不等式</p>
          </li>
          <li>
            <p><span>065</span></p>
            <p><span>065-066</span></p>
          </li>
        </ul>

        <div class="padding-116">72</div>
        <div class="padding-116">
          <h2 id="b014">单元检测<span class="fontsz1">＞＞＞＞＞＞＞＞</span></h2>
          <div class="bj">
            <examinations :cardList="questionData[72]" :hideCollect="true" sourceType="json" v-if="questionData">
            </examinations>
          </div>
        </div>
      </div>
    </div>
    <!-- 066 -->
    <div class="page-box" page="73">
      <div v-if="showPageList.indexOf(73) > -1">
        <ul class="page-header-odd fl al-end">
          <li>066</li>
          <li>数学.基础模块</li>
          <li>上册</li>
        </ul>
        <div class="padding-116">73</div>
      </div>
    <div class="page-box hidePage" page="73">
    </div>
    <!-- 解题思路弹窗 -->
    <el-dialog :visible.sync="thinkingDialog" width="40%" :append-to-body="true" :show-close="false"
      @close="closeDialog" class="thinkDialog">
      <div slot="title" class="think-header"
        style="padding: 0; text-align: center; color: #333;display:flex;justify-content: center;">
        <span style=""> 分析 </span>
        <svg style="position: absolute; right:10px;cursor: pointer;" @click="thinkingDialog = false" t="1718596022986"
          class="icon" viewBox="0 0 1024 1024" version="1.1" xmlns="http://www.w3.org/2000/svg" p-id="4252" width="20"
          height="20" xmlns:xlink="http://www.w3.org/1999/xlink">
          <path
            d="M176.661601 817.172881C168.472798 825.644055 168.701706 839.149636 177.172881 847.338438 185.644056 855.527241 199.149636 855.298332 207.338438 846.827157L826.005105 206.827157C834.193907 198.355983 833.964998 184.850403 825.493824 176.661601 817.02265 168.472798 803.517069 168.701706 795.328267 177.172881L176.661601 817.172881Z"
            fill="#979797" p-id="4253"></path>
          <path
            d="M795.328267 846.827157C803.517069 855.298332 817.02265 855.527241 825.493824 847.338438 833.964998 839.149636 834.193907 825.644055 826.005105 817.172881L207.338438 177.172881C199.149636 168.701706 185.644056 168.472798 177.172881 176.661601 168.701706 184.850403 168.472798 198.355983 176.661601 206.827157L795.328267 846.827157Z"
            fill="#979797" p-id="4254"></path>
        </svg>
      </div>
      <ul>
        <li v-for="(item, index) in thinkData" :key="index">
          <div v-if="index <= showIndex" style="display: flex">
            <span style="position: relative">
              <span style="position: absolute; top: 16px; left: 13px; color: #fff">{{ index + 1 }}</span>
              <img src="../../assets/images/icon/blue-group.png" alt="" style="margin-right: 10px"
                v-if="index < thinkOne.length - 1" />
              <img src="../../assets/images/icon/blue.png" alt="" v-if="index == thinkOne.length - 1"
                style="margin-right: 10px" />
            </span>
            <p class="txt-p" v-html="item"></p>
          </div>
        </li>
      </ul>
      <div @click="changeNext" style="
          display: flex;
          flex-direction: column;
          align-items: center;
          justify-content: center;
        ">
        <img src="../../assets/images/icon/mouse.png" alt="" v-if="showIndex < thinkData.length - 1" />
        <svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" t="1710234570135"
          class="icon" viewBox="0 0 1024 1024" version="1.1" p-id="5067" width="15" height="15">
          <path
            d="M2.257993 493.371555 415.470783 906.584344 512 1003.113561 608.529217 906.584344 1021.742007 493.371555 925.212789 396.842337 512 810.055127 98.787211 396.842337Z"
            fill="#1296db" p-id="5068" />
          <path
            d="M2.257993 117.980154 415.470783 531.192944 512 627.722161 608.529217 531.192944 1021.742007 117.980154 925.212789 21.450937 512 434.663727 98.787211 21.450937Z"
            fill="#1296db" p-id="5069" />
        </svg>
      </div>
    </el-dialog>
  </div>
</template>

<script>
const handleShow = (num) => {
  const obj = {}
  for (let index = 0; index < num; index++) {
    obj['isShowAnswer' + index] = false
  }
  return obj
}
const showObj = handleShow(30)
import paint from '@/components/paint/index.vue'
import examinations from '@/components/examinations/index.vue'
export default {
  name: '',
  name: "",
  props: {
    showPageList: {
      type: Array,
      default: [],
    },
    questionData: {
      type: Object,
    },
  },
  components: {},
  components: { examinations, paint },
  data() {
    return {}
    return {
      collectImg: require('../../assets/images/icon/heart.png'),
      collectCheck: require('../../assets/images/icon/heart-check.png'),
      thinkingDialog: false,
      showIndex: 0,
      thinkData: [],
      thinkOne: [
        '①根据<i>x</i><sup>2</sup>的系数判断函数图像（抛物线）的开口方向；',
        '②用判别式判定出一元二次方程<i>x</i><sup>2</sup>-2<i>x</i>-3=0的解的情况，从而确定二次函数<i>y</i>=<i>x</i><sup>2</sup>-2<i>x</i>-3的图像与<i>x</i>轴的交点个数和交点坐标；',
        '③计算二次函数图像的顶点坐标、与<i>y</i>轴的交点坐标；',
        '④求出二次函数图像的对称轴方程，并利用函数图像的对称性再找出一些点；⑤最后根据上述信息画出函数图像.',
        '画出图像后，<i>y</i>=0，<i>y</i>＞0，<i>y</i>＜0分别对应函数图像与<i>x</i>轴相交、函数图像在<i>x</i>轴上方、函数图像在<i>x</i>轴下方三种情形，根据图像完成（2）（3）两个问题.'
      ],
      thinkTwo:[
        '由（<i>x</i>+1）<sup>2</sup>≥4得<i>x</i><sup>2</sup>+2<i>x</i>+1≥4，即<i>x</i><sup>2</sup>+2<i>x</i>-3≥0，从而可以利用二次函数<i>y</i>=<i>x</i><sup>2</sup>+2<i>x</i>-3的图像进行求解；注意到4=2<sup>2</sup>，也可以考虑将（<i>x</i>+1）<sup>2</sup>≥4整理为（<i>x</i>+1）<sup>2</sup>-4≥0，并使用平方差公式，即（<i>x</i>+1）<sup>2</sup>-2<sup>2</sup>≥0，得到（<i>x</i>+3）（<i>x</i>-1）≥0，此时可以借助上面的结论直接求解.下面我们将使用后一种方法进行求解.'
      ],
      thinkThree:[
        '利润=（销售单价-成本单价）×销售量.降价过程中，单价降低能够使销售量变大，但也使销售单价与成本单价的差减小，所以降价的范围应保证利润不低于促销前.'
      ],
      isShowAnswer: false,
      isShowAnswerOne: false,
      ...showObj
    };
  },
  computed: {},
  watch: {},
  created() { },
  mounted() { },
  methods: {},
}
  mounted() {
    console.log(2, this);
  },
  methods: {
    openDialog(queryData) {
      this.thinkData = queryData
      this.thinkingDialog = !this.thinkingDialog
    },
    closeDialog() {
      this.showIndex = 0
    },
    changeNext() {
      if (this.showIndex < this.thinkData.length - 1) this.showIndex = this.showIndex + 1
    }
  },
};
</script>

<style lang="less" scoped></style>
<style lang="less" scoped>
.pr {
  position: relative;
}

.pa-bk {
  position: absolute;
  right: 45px;
  top: 0;
  width: 140px;
}

.question-textarea {
  margin-left: 20px;
  width: 94%;
  border-color: #DCDFE6;
}

.table-answer-box {
  math {
    width: max-content;
    height: 36px;
  }
}

li {
  list-style: none;
}
</style>