WEBVTT

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欢迎收看 这是二次公式第二节

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上一节但愿没把大家弄迷糊

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下面看几个例子 希望能增进理解

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先回顾下二次公式

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二次公式也就是说

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解方程Ax2+Bx+C=0时

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由于曲线同x轴通常相交两次

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解通常也有两个

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解为x=[-B±根号(B2-4AC)]/(2A)

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解为x=[-B±根号(B2-4AC)]/(2A)

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做题比耍嘴皮子会容易些

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这是个2

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假设有方程-9x2-9x+6=0

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这题中 A是什么

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A是x2项系数

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x2项在这里 系数为-9

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写一下 A=-9 那B呢

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B是x项系数 这一项

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B也是-9

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C是常数项 这里是6

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C=6

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将这些值代入到二次公式中

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-B即-(-9)

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±根号下 B2即(-9)2 也就是81

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-4AC 即-4?(-9)?6

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整个除以2倍-9 即-18

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2倍-9也就是2A 下面化简

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-(-9)也就是正9

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±根号下 第一项是81

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然后是-4乘以-9

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-4乘以-9是正36

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正36乘以6 30×6=180

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180+36=216

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216 对不对

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180+36=216

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整个除以2A

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2A是-18 继续化简

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有9±根号(81+216)

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即80+217=297

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所有除以-18

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通常 二次公式最麻烦的

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是化简这个式子

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这个根式必须处理

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看看

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首先容易看出 这个数能被9整除

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因为所有位数相加是9的倍数

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2+9+7=18

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看一下它是9乘以多少

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在这边来做 免得弄乱

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297除以9

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3 余27

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结果是33

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这也就等于[9±根号(9?33)]/(-18)

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9是完全平方数

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这就是我把9提出来的原因

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只有完全平方数才能提出根号

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我讲指数法则时讲过

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这等于(9±3倍根号33)/(-18) 基本完成

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这等于(9±3倍根号33)/(-18) 基本完成

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还可以化简

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9 3 -18都是3的倍数

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都除以3

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得到(3±根号33)/(-6)

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搞定

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可见 二次公式最复杂的工作是化简

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可见 二次公式最复杂的工作是化简

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我的板书有点混乱

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我总结一下 方程是-9x2-9x+6=0

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求出两个x值满足方程

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求出两个x值满足方程

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一个值是x=(3+根号33)/(-6)

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另一个值是x=(3-根号33)/(-6)

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想想为什么会是±

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这是因为开根号

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会出现正平方根和负平方根

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再看个例子

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但愿这个会简单点

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-8x2+5x+9=0

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假设二次公式我们已经记住

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你可以在纸上默写一下

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这必须记住

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公式中 B是5

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这里等于0没写 首先是-B

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-5 加减 根号下有B2

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即52=25

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-4AC 即-4?(-8)?9

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整个除以2A

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A是-8 所以是除以-16

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然后化简

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这是-5±

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根号下 25

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4乘以8是32 负号抵消

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有正32乘以9

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32?9 先算30?9是270 所以是288

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所有这些除以-16 继续化简

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-5± 根号下 25+288=313

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整个除以-16

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我敢基本保证这是对的

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我没检验

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313不是完全平方数也没有完全平方数因数

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313不是完全平方数也没有完全平方数因数

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它其实是质数

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这是需要判别的

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这样 这就是最简形式了

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总共有两个解

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两个x值满足方程

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一个是x=(-5+根号313)/(-16)

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一个是x=(-5+根号313)/(-16)

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一个是x=(-5-根号313)/(-16)

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一个是x=(-5-根号313)/(-16)

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但愿这两个例子能让大家

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更好地理解二次公式

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后面还有视频

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掌握这些以后 我会教大家

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如何解根号下是负数的情况

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如何解根号下是负数的情况

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很有趣

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希望大家能理解并多做练习

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这部分内容不怎么容易理解

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祝开心 再会

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