[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.89,0:00:05.66,Default,,0000,0000,0000,,欢迎收看 这是二次公式第二节
Dialogue: 0,0:00:05.66,0:00:08.87,Default,,0000,0000,0000,,上一节但愿没把大家弄迷糊
Dialogue: 0,0:00:08.87,0:00:12.77,Default,,0000,0000,0000,,下面看几个例子 希望能增进理解
Dialogue: 0,0:00:12.77,0:00:16.38,Default,,0000,0000,0000,,先回顾下二次公式
Dialogue: 0,0:00:16.38,0:00:19.65,Default,,0000,0000,0000,,二次公式也就是说
Dialogue: 0,0:00:19.65,0:00:31.59,Default,,0000,0000,0000,,解方程Ax2+Bx+C=0时
Dialogue: 0,0:00:31.59,0:00:35.44,Default,,0000,0000,0000,,由于曲线同x轴通常相交两次
Dialogue: 0,0:00:35.44,0:00:38.97,Default,,0000,0000,0000,,解通常也有两个
Dialogue: 0,0:00:38.97,0:00:47.61,Default,,0000,0000,0000,,解为x=[-B±根号(B2-4AC)]/(2A)
Dialogue: 0,0:00:47.61,0:01:00.27,Default,,0000,0000,0000,,解为x=[-B±根号(B2-4AC)]/(2A)
Dialogue: 0,0:01:00.27,0:01:02.49,Default,,0000,0000,0000,,做题比耍嘴皮子会容易些
Dialogue: 0,0:01:02.49,0:01:04.62,Default,,0000,0000,0000,,这是个2
Dialogue: 0,0:01:04.62,0:01:19.95,Default,,0000,0000,0000,,假设有方程-9x2-9x+6=0
Dialogue: 0,0:01:19.95,0:01:22.23,Default,,0000,0000,0000,,这题中 A是什么
Dialogue: 0,0:01:22.23,0:01:25.41,Default,,0000,0000,0000,,A是x2项系数
Dialogue: 0,0:01:25.41,0:01:29.82,Default,,0000,0000,0000,,x2项在这里 系数为-9
Dialogue: 0,0:01:29.82,0:01:35.40,Default,,0000,0000,0000,,写一下 A=-9 那B呢
Dialogue: 0,0:01:35.40,0:01:39.18,Default,,0000,0000,0000,,B是x项系数 这一项
Dialogue: 0,0:01:39.18,0:01:43.22,Default,,0000,0000,0000,,B也是-9
Dialogue: 0,0:01:43.22,0:01:47.14,Default,,0000,0000,0000,,C是常数项 这里是6
Dialogue: 0,0:01:47.14,0:01:49.55,Default,,0000,0000,0000,,C=6
Dialogue: 0,0:01:49.55,0:01:53.26,Default,,0000,0000,0000,,将这些值代入到二次公式中
Dialogue: 0,0:01:53.26,0:02:00.78,Default,,0000,0000,0000,,-B即-(-9)
Dialogue: 0,0:02:00.78,0:02:10.03,Default,,0000,0000,0000,,±根号下 B2即(-9)2 也就是81
Dialogue: 0,0:02:10.03,0:02:19.48,Default,,0000,0000,0000,,-4AC 即-4×(-9)×6
Dialogue: 0,0:02:19.48,0:02:25.63,Default,,0000,0000,0000,,整个除以2倍-9 即-18
Dialogue: 0,0:02:25.63,0:02:33.76,Default,,0000,0000,0000,,2倍-9也就是2A 下面化简
Dialogue: 0,0:02:33.76,0:02:37.93,Default,,0000,0000,0000,,-(-9)也就是正9
Dialogue: 0,0:02:37.93,0:02:46.48,Default,,0000,0000,0000,,±根号下 第一项是81
Dialogue: 0,0:02:46.48,0:02:50.27,Default,,0000,0000,0000,,然后是-4乘以-9
Dialogue: 0,0:02:50.27,0:02:53.47,Default,,0000,0000,0000,,-4乘以-9是正36
Dialogue: 0,0:02:53.47,0:03:01.33,Default,,0000,0000,0000,,正36乘以6 30×6=180
Dialogue: 0,0:03:01.33,0:03:07.89,Default,,0000,0000,0000,,180+36=216
Dialogue: 0,0:03:07.89,0:03:10.98,Default,,0000,0000,0000,,216 对不对
Dialogue: 0,0:03:10.98,0:03:14.49,Default,,0000,0000,0000,,180+36=216
Dialogue: 0,0:03:14.49,0:03:16.84,Default,,0000,0000,0000,,整个除以2A
Dialogue: 0,0:03:16.84,0:03:20.74,Default,,0000,0000,0000,,2A是-18 继续化简
Dialogue: 0,0:03:20.74,0:03:28.09,Default,,0000,0000,0000,,有9±根号(81+216)
Dialogue: 0,0:03:28.09,0:03:38.04,Default,,0000,0000,0000,,即80+217=297
Dialogue: 0,0:03:38.04,0:03:41.90,Default,,0000,0000,0000,,所有除以-18
Dialogue: 0,0:03:41.90,0:03:45.02,Default,,0000,0000,0000,,通常 二次公式最麻烦的
Dialogue: 0,0:03:45.02,0:03:47.72,Default,,0000,0000,0000,,是化简这个式子
Dialogue: 0,0:03:47.72,0:03:50.86,Default,,0000,0000,0000,,这个根式必须处理
Dialogue: 0,0:03:50.86,0:03:53.09,Default,,0000,0000,0000,,看看
Dialogue: 0,0:03:53.09,0:03:56.49,Default,,0000,0000,0000,,首先容易看出 这个数能被9整除
Dialogue: 0,0:03:56.49,0:03:59.26,Default,,0000,0000,0000,,因为所有位数相加是9的倍数
Dialogue: 0,0:03:59.26,0:04:02.51,Default,,0000,0000,0000,,2+9+7=18
Dialogue: 0,0:04:02.51,0:04:04.60,Default,,0000,0000,0000,,看一下它是9乘以多少
Dialogue: 0,0:04:04.60,0:04:07.15,Default,,0000,0000,0000,,在这边来做 免得弄乱
Dialogue: 0,0:04:07.15,0:04:09.45,Default,,0000,0000,0000,,297除以9
Dialogue: 0,0:04:13.63,0:04:16.19,Default,,0000,0000,0000,,3 余27
Dialogue: 0,0:04:16.19,0:04:19.04,Default,,0000,0000,0000,,结果是33
Dialogue: 0,0:04:19.04,0:04:31.11,Default,,0000,0000,0000,,这也就等于[9±根号(9?33)]/(-18)
Dialogue: 0,0:04:31.11,0:04:32.47,Default,,0000,0000,0000,,9是完全平方数
Dialogue: 0,0:04:32.47,0:04:34.98,Default,,0000,0000,0000,,这就是我把9提出来的原因
Dialogue: 0,0:04:34.98,0:04:37.39,Default,,0000,0000,0000,,只有完全平方数才能提出根号
Dialogue: 0,0:04:37.39,0:04:40.41,Default,,0000,0000,0000,,我讲指数法则时讲过
Dialogue: 0,0:04:40.41,0:04:48.16,Default,,0000,0000,0000,,这等于(9±3倍根号33)/(-18) 基本完成
Dialogue: 0,0:04:48.16,0:04:54.57,Default,,0000,0000,0000,,这等于(9±3倍根号33)/(-18) 基本完成
Dialogue: 0,0:04:54.57,0:04:56.26,Default,,0000,0000,0000,,还可以化简
Dialogue: 0,0:04:56.26,0:05:00.65,Default,,0000,0000,0000,,9 3 -18都是3的倍数
Dialogue: 0,0:05:00.65,0:05:02.27,Default,,0000,0000,0000,,都除以3
Dialogue: 0,0:05:02.27,0:05:14.37,Default,,0000,0000,0000,,得到(3±根号33)/(-6)
Dialogue: 0,0:05:14.37,0:05:15.61,Default,,0000,0000,0000,,搞定
Dialogue: 0,0:05:15.61,0:05:17.01,Default,,0000,0000,0000,,可见 二次公式最复杂的工作是化简
Dialogue: 0,0:05:17.01,0:05:20.11,Default,,0000,0000,0000,,可见 二次公式最复杂的工作是化简
Dialogue: 0,0:05:20.11,0:05:22.75,Default,,0000,0000,0000,,我的板书有点混乱
Dialogue: 0,0:05:22.75,0:05:30.55,Default,,0000,0000,0000,,我总结一下 方程是-9x2-9x+6=0
Dialogue: 0,0:05:30.55,0:05:34.20,Default,,0000,0000,0000,,求出两个x值满足方程
Dialogue: 0,0:05:35.97,0:05:42.10,Default,,0000,0000,0000,,一个值是x=(3+根号33)/(-6)
Dialogue: 0,0:05:42.10,0:05:50.16,Default,,0000,0000,0000,,另一个值是x=(3-根号33)/(-6)
Dialogue: 0,0:05:50.16,0:05:53.37,Default,,0000,0000,0000,,想想为什么会是±
Dialogue: 0,0:05:53.37,0:05:55.49,Default,,0000,0000,0000,,这是因为开根号
Dialogue: 0,0:05:55.49,0:05:59.55,Default,,0000,0000,0000,,会出现正平方根和负平方根
Dialogue: 0,0:05:59.55,0:06:02.18,Default,,0000,0000,0000,,再看个例子
Dialogue: 0,0:06:02.18,0:06:05.89,Default,,0000,0000,0000,,但愿这个会简单点
Dialogue: 0,0:06:09.21,0:06:21.00,Default,,0000,0000,0000,,-8x2+5x+9=0
Dialogue: 0,0:06:21.00,0:06:23.15,Default,,0000,0000,0000,,假设二次公式我们已经记住
Dialogue: 0,0:06:23.15,0:06:25.31,Default,,0000,0000,0000,,你可以在纸上默写一下
Dialogue: 0,0:06:25.31,0:06:26.63,Default,,0000,0000,0000,,这必须记住
Dialogue: 0,0:06:26.63,0:06:31.63,Default,,0000,0000,0000,,公式中 B是5
Dialogue: 0,0:06:31.63,0:06:34.16,Default,,0000,0000,0000,,这里等于0没写 首先是-B
Dialogue: 0,0:06:34.16,0:06:39.79,Default,,0000,0000,0000,,-5 加减 根号下有B2
Dialogue: 0,0:06:39.79,0:06:44.03,Default,,0000,0000,0000,,即52=25
Dialogue: 0,0:06:44.03,0:06:53.82,Default,,0000,0000,0000,,-4AC 即-4×(-8)×9
Dialogue: 0,0:06:53.82,0:06:56.40,Default,,0000,0000,0000,,整个除以2A
Dialogue: 0,0:06:56.40,0:07:00.32,Default,,0000,0000,0000,,A是-8 所以是除以-16
Dialogue: 0,0:07:00.32,0:07:04.09,Default,,0000,0000,0000,,然后化简
Dialogue: 0,0:07:04.09,0:07:09.44,Default,,0000,0000,0000,,这是-5±
Dialogue: 0,0:07:09.44,0:07:14.62,Default,,0000,0000,0000,,根号下 25
Dialogue: 0,0:07:14.62,0:07:18.22,Default,,0000,0000,0000,,4乘以8是32 负号抵消
Dialogue: 0,0:07:18.22,0:07:21.52,Default,,0000,0000,0000,,有正32乘以9
Dialogue: 0,0:07:21.52,0:07:37.49,Default,,0000,0000,0000,,32×9 先算30?9是270 所以是288
Dialogue: 0,0:07:37.49,0:07:42.56,Default,,0000,0000,0000,,所有这些除以-16 继续化简
Dialogue: 0,0:07:42.56,0:07:51.34,Default,,0000,0000,0000,,-5± 根号下 25+288=313
Dialogue: 0,0:07:56.95,0:08:00.23,Default,,0000,0000,0000,,整个除以-16
Dialogue: 0,0:08:00.23,0:08:03.43,Default,,0000,0000,0000,,我敢基本保证这是对的
Dialogue: 0,0:08:03.43,0:08:04.57,Default,,0000,0000,0000,,我没检验
Dialogue: 0,0:08:04.57,0:08:10.37,Default,,0000,0000,0000,,313不是完全平方数也没有完全平方数因数
Dialogue: 0,0:08:10.37,0:08:11.69,Default,,0000,0000,0000,,313不是完全平方数也没有完全平方数因数
Dialogue: 0,0:08:11.69,0:08:13.67,Default,,0000,0000,0000,,它其实是质数
Dialogue: 0,0:08:13.67,0:08:15.60,Default,,0000,0000,0000,,这是需要判别的
Dialogue: 0,0:08:15.60,0:08:19.30,Default,,0000,0000,0000,,这样 这就是最简形式了
Dialogue: 0,0:08:19.30,0:08:21.84,Default,,0000,0000,0000,,总共有两个解
Dialogue: 0,0:08:21.84,0:08:24.94,Default,,0000,0000,0000,,两个x值满足方程
Dialogue: 0,0:08:24.94,0:08:30.75,Default,,0000,0000,0000,,一个是x=(-5+根号313)/(-16)
Dialogue: 0,0:08:30.75,0:08:35.83,Default,,0000,0000,0000,,一个是x=(-5+根号313)/(-16)
Dialogue: 0,0:08:35.83,0:08:44.11,Default,,0000,0000,0000,,一个是x=(-5-根号313)/(-16)
Dialogue: 0,0:08:44.11,0:08:49.66,Default,,0000,0000,0000,,一个是x=(-5-根号313)/(-16)
Dialogue: 0,0:08:49.66,0:08:51.76,Default,,0000,0000,0000,,但愿这两个例子能让大家
Dialogue: 0,0:08:51.76,0:08:53.94,Default,,0000,0000,0000,,更好地理解二次公式
Dialogue: 0,0:08:53.94,0:08:55.86,Default,,0000,0000,0000,,后面还有视频
Dialogue: 0,0:08:55.86,0:08:58.23,Default,,0000,0000,0000,,掌握这些以后 我会教大家
Dialogue: 0,0:08:58.23,0:09:00.37,Default,,0000,0000,0000,,如何解根号下是负数的情况
Dialogue: 0,0:09:00.37,0:09:01.91,Default,,0000,0000,0000,,如何解根号下是负数的情况
Dialogue: 0,0:09:01.91,0:09:03.14,Default,,0000,0000,0000,,很有趣
Dialogue: 0,0:09:03.14,0:09:06.76,Default,,0000,0000,0000,,希望大家能理解并多做练习
Dialogue: 0,0:09:06.76,0:09:10.37,Default,,0000,0000,0000,,这部分内容不怎么容易理解
Dialogue: 0,0:09:10.37,0:09:13.14,Default,,0000,0000,0000,,祝开心 再会
Dialogue: 0,0:00:01.00,0:00:15.00,Default,,0000,0000,0000,,本字幕由网易公开课提供，更多课程请到http//open.163.com
Dialogue: 0,0:00:17.07,0:00:25.07,Default,,0000,0000,0000,,网易公开课官方微博 http://t.163.com/163open