总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (x-1)(x-4)(x-9)-3*2*6-3*2*6-9(x-4)-4(x-9)-36(x-1) = 0 的解.
题型:方程
解:原方程:| | ( | x | − | 1 | ) | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 3 | × | 2 | × | 6 | − | 3 | × | 2 | × | 6 | − | 9 | ( | x | − | 4 | ) | − | 4 | = | 0 |
| 方程左边 = | ( | x | − | 1 | ) | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 36 | − | 36 | − | 9 | ( | x | − | 4 | ) | − | 4 | ( | x | − | 9 | ) | − | 36 | ( | x | − | 1 | ) |
| = | ( | x | − | 1 | ) | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 72 | − | 9 | ( | x | − | 4 | ) | − | 4 | ( | x | − | 9 | ) | − | 36 | ( | x | − | 1 | ) |
方程化为:
| | ( | x | − | 1 | ) | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 72 | − | 9 | ( | x | − | 4 | ) | − | 4 | ( | x | − | 9 | ) | − | 36 | ( | x | − | 1 | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | x | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 1 | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 72 | − | 9 | ( | x | − | 4 | ) | − | 4 | ( | x | − | 9 | ) | − | 36 |
| = | x | x | ( | x | − | 9 | ) | − | x | × | 4 | ( | x | − | 9 | ) | − | 1 | ( | x | − | 4 | ) | ( | x | − | 9 | ) | − | 72 | − | 9 | ( | x | − | 4 | ) |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | ( | x | − | 9 | ) | − | 1 | ( | x | − | 4 | ) | ( | x | − | 9 | ) |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | x | × | 4 | × | 9 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | x | × | 36 | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 45 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 45 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 45 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 49 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 49 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 49 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 40 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 40 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 40 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 36 | x | − | 1 |
| = | x | x | x | − | x | x | × | 9 | − | x | × | 4 | x | + | 0 | x | − | 1 |
方程化为一般式后,用因式分解法化为:
( x - 0 )( x - 0 )( x - 14 )=0
由
x - 0 = 0
x - 0 = 0
x - 14 = 0
得:
x1=0
x2=0
x3=14
有 3个解。
解程的详细方法请参阅:《方程的解法》
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