1
00:00:00,650 --> 00:00:02,700
要解二次方程 －3x 的平方加上

2
00:00:02,700 --> 00:00:07,620
10x 减去 3 等于 0。

3
00:00:07,620 --> 00:00:09,560
这个方程已经是标准式了。

4
00:00:09,560 --> 00:00:11,060
有很多解法。

5
00:00:11,060 --> 00:00:13,597
如果采用二次方程求解的公式一定可以解出来。

6
00:00:13,597 --> 00:00:14,680
我把方程抄下来。

7
00:00:14,680 --> 00:00:19,435
方程为－3x 的平方加上 10x 减去 3 等于 0。

8
00:00:19,435 --> 00:00:20,810
我打算用二次方程的公式

9
00:00:20,810 --> 00:00:22,720
来解两次，以说明只要我们

10
00:00:22,720 --> 00:00:25,350
正确地使用公式，

11
00:00:25,350 --> 00:00:26,850
就一定能得到该

12
00:00:26,850 --> 00:00:29,900
方程的正确且

13
00:00:29,900 --> 00:00:31,370
一致的解答。

14
00:00:31,370 --> 00:00:34,322
在眼前这个格式的方程里面, a, b, c 是多少？

15
00:00:34,322 --> 00:00:36,780
我们先来谈谈二次方程

16
00:00:36,780 --> 00:00:37,450
的解题公式是什么。

17
00:00:37,450 --> 00:00:38,730
从这里开始比较好。

18
00:00:38,730 --> 00:00:40,640
二次方程的解题公式

19
00:00:40,640 --> 00:00:43,170
就是面对一个二次方程，

20
00:00:43,170 --> 00:00:48,320
格式为 a x 平方加上 b x 再加上 c 等于 0，就是用标准格式来表示，

21
00:00:48,320 --> 00:00:52,360
它的解就是 x 等于 －b

22
00:00:52,360 --> 00:00:55,630
加上或减去 b 的平方减去 4a c的平方根，

23
00:00:55,630 --> 00:01:02,430
然后再除以 2a。

24
00:01:02,430 --> 00:01:05,239
而这个公式源于解二次方程的

25
00:01:05,239 --> 00:01:06,410
构建平方法。

26
00:01:06,410 --> 00:01:09,914
因此这个方法并不深奥，我在其它的视频里已经推导过了。

27
00:01:09,914 --> 00:01:11,330
这就是解二次方程的公式。

28
00:01:11,330 --> 00:01:12,910
这个公式可以得到两个解，

29
00:01:12,910 --> 00:01:14,890
因为这里有正负

30
00:01:14,890 --> 00:01:16,680
两个平方根。

31
00:01:16,680 --> 00:01:19,750
在这里把它应用于本例 － 本例里面，

32
00:01:19,750 --> 00:01:26,890
a 等于 －3，b 等于 10，

33
00:01:26,890 --> 00:01:31,000
c 等于 －3。

34
00:01:31,000 --> 00:01:33,240
所以在这里运用解二次方程的公式，

35
00:01:33,240 --> 00:01:36,526
所得的解为 x 等于一个代数式，

36
00:01:36,526 --> 00:01:37,530
其分子部分第一项 －b，b 就是 10。

37
00:01:37,530 --> 00:01:42,800
－b 就是 －10，然后加或减一个根式，

38
00:01:42,800 --> 00:01:44,690
里面第一项是 b 平方。

39
00:01:44,690 --> 00:01:45,460


40
00:01:45,460 --> 00:01:50,650


41
00:01:50,650 --> 00:01:54,387


42
00:01:54,387 --> 00:01:55,470


43
00:01:55,470 --> 00:01:58,930


44
00:01:58,930 --> 00:02:01,100


45
00:02:01,100 --> 00:02:02,860


46
00:02:02,860 --> 00:02:05,540


47
00:02:05,540 --> 00:02:07,660


48
00:02:07,660 --> 00:02:14,710


49
00:02:14,710 --> 00:02:16,080


50
00:02:16,080 --> 00:02:18,280


51
00:02:18,280 --> 00:02:19,530


52
00:02:19,530 --> 00:02:21,610


53
00:02:21,610 --> 00:02:23,860


54
00:02:23,860 --> 00:02:27,310


55
00:02:27,310 --> 00:02:31,830


56
00:02:31,830 --> 00:02:33,900


57
00:02:33,900 --> 00:02:35,939


58
00:02:35,939 --> 00:02:38,230


59
00:02:38,230 --> 00:02:43,940


60
00:02:43,940 --> 00:02:45,620


61
00:02:45,620 --> 00:02:48,210


62
00:02:48,210 --> 00:02:52,560


63
00:02:52,560 --> 00:02:54,570


64
00:02:54,570 --> 00:02:56,330


65
00:02:56,330 --> 00:02:58,940


66
00:02:58,940 --> 00:03:00,840


67
00:03:00,840 --> 00:03:04,610


68
00:03:04,610 --> 00:03:08,030


69
00:03:08,030 --> 00:03:10,070


70
00:03:10,070 --> 00:03:13,490


71
00:03:13,490 --> 00:03:16,930


72
00:03:16,930 --> 00:03:19,380


73
00:03:19,380 --> 00:03:22,492


74
00:03:22,492 --> 00:03:24,700


75
00:03:24,700 --> 00:03:25,740


76
00:03:25,740 --> 00:03:27,280


77
00:03:27,280 --> 00:03:30,120


78
00:03:30,120 --> 00:03:31,876


79
00:03:31,876 --> 00:03:33,250


80
00:03:33,250 --> 00:03:37,010


81
00:03:37,010 --> 00:03:39,270


82
00:03:39,270 --> 00:03:45,000


83
00:03:45,000 --> 00:03:46,900


84
00:03:46,900 --> 00:03:51,990


85
00:03:51,990 --> 00:03:54,430


86
00:03:54,430 --> 00:03:56,400


87
00:03:56,400 --> 00:04:00,560


88
00:04:00,560 --> 00:04:02,460


89
00:04:02,460 --> 00:04:05,300


90
00:04:05,300 --> 00:04:07,950


91
00:04:07,950 --> 00:04:12,110


92
00:04:12,110 --> 00:04:16,070


93
00:04:16,070 --> 00:04:17,980


94
00:04:17,980 --> 00:04:20,250


95
00:04:20,250 --> 00:04:21,990


96
00:04:21,990 --> 00:04:28,030


97
00:04:28,030 --> 00:04:30,660


98
00:04:30,660 --> 00:04:32,210


99
00:04:32,210 --> 00:04:36,420


100
00:04:36,420 --> 00:04:38,310


101
00:04:38,310 --> 00:04:41,300


102
00:04:41,300 --> 00:04:43,100


103
00:04:43,100 --> 00:04:46,280


104
00:04:46,280 --> 00:04:50,300