总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (x+3)*(x+2)*(x+5)+x*(x+3)*(x+5)+x*(x+2)*(x+5) = x*(x+3)*(x+2) 的解.
题型:方程
解:原方程:| | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | x | + | 5 | ) | + | x | ( | x | + | 3 | ) | ( | x | + | 5 | ) | + | x | ( | x | + | 2 | ) | ( | x | + | 5 | ) | = | x | ( | x | + | 3 | ) | ( | x | + | 2 | ) |
去掉方程左边的括号:
| 方程左边 = | x | ( | x | + | 2 | ) | ( | x | + | 5 | ) | + | 3 | ( | x | + | 2 | ) | ( | x | + | 5 | ) | + | x | ( | x | + | 3 | ) | ( | x | + | 5 | ) | + | x | ( | x | + | 2 | ) | ( | x | + | 5 | ) |
| = | x | x | ( | x | + | 5 | ) | + | x | × | 2 | ( | x | + | 5 | ) | + | 3 | ( | x | + | 2 | ) | ( | x | + | 5 | ) | + | x | ( | x | + | 3 | ) | ( | x | + | 5 | ) |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | ( | x | + | 5 | ) | + | 3 | ( | x | + | 2 | ) | ( | x | + | 5 | ) |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | x | × | 2 | × | 5 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | x | × | 10 | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 10 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 10 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 10 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 10 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 25 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 25 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 25 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 31 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 31 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 31 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 31 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 31 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 46 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 46 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 46 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 46 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 46 | x | + | 3 |
| = | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 56 | x | + | 3 |
方程化为:
| | x | x | x | + | x | x | × | 5 | + | x | × | 2 | x | + | 56 | x | + | 3 | = | x | ( | x | + | 3 | ) | ( | x | + | 2 | ) |
去掉方程右边的括号:
| 方程右边 = | x | x | ( | x | + | 2 | ) | + | x | × | 3 | ( | x | + | 2 | ) |
方程的解为:
x1≈-6.517113 ,保留6位小数
x2≈-2.596424 ,保留6位小数
x3≈-0.886462 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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