总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (x-5)*(x-8)*(x-3)*(x-2)-2*(x-5)*(x-8)+4*(x-3)*(x-2)-8 = 0 的解.
题型:方程
解:原方程:| | ( | x | − | 5 | ) | ( | x | − | 8 | ) | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | 2 | ( | x | − | 5 | ) | ( | x | − | 8 | ) | + | 4 | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | 8 | = | 0 |
去掉方程左边的括号:
| 方程左边 = | x | ( | x | − | 8 | ) | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | 5 | ( | x | − | 8 | ) | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | 2 | ( | x | − | 5 | ) | ( | x | − | 8 | ) | + | 4 |
| = | x | x | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | x | × | 8 | ( | x | − | 3 | ) | ( | x | − | 2 | ) | − | 5 | ( | x | − | 8 | ) | ( | x | − | 3 | ) | ( | x | − | 2 | ) |
| = | x | x | x | ( | x | − | 2 | ) | − | x | x | × | 3 | ( | x | − | 2 | ) | − | x | × | 8 | ( | x | − | 3 | ) | ( | x | − | 2 | ) |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | ( | x | − | 2 | ) |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
| = | x | x | x | x | − | x | x | x | × | 2 | − | x | x | × | 3 | x |
方程化为一般式后,用因式分解法化为:
( x - 1 )( x - 4 )=0
由
x - 1 = 0
x - 4 = 0
得:
x1=1
x2=4
有 2个解。
解一元二次方程的详细方法请参阅:《一元二次方程的解法》
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