总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (s+2)(s-1)(s+20)+s(s+20)(s+2)+s(s-1)(s+2) = s(s+20)(s-1) 的解.
题型:方程
解:原方程:| | ( | s | + | 2 | ) | ( | s | − | 1 | ) | ( | s | + | 20 | ) | + | s | ( | s | + | 20 | ) | ( | s | + | 2 | ) | + | s | ( | s | − | 1 | ) | ( | s | + | 2 | ) | = | s | ( | s | + | 20 | ) | ( | s | − | 1 | ) |
去掉方程左边的括号:
| 方程左边 = | s | ( | s | − | 1 | ) | ( | s | + | 20 | ) | + | 2 | ( | s | − | 1 | ) | ( | s | + | 20 | ) | + | s | ( | s | + | 20 | ) | ( | s | + | 2 | ) | + | s | ( | s | − | 1 | ) | ( | s | + | 2 | ) |
| = | s | s | ( | s | + | 20 | ) | − | s | × | 1 | ( | s | + | 20 | ) | + | 2 | ( | s | − | 1 | ) | ( | s | + | 20 | ) | + | s | ( | s | + | 20 | ) | ( | s | + | 2 | ) |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | ( | s | + | 20 | ) | + | 2 | ( | s | − | 1 | ) | ( | s | + | 20 | ) |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | s | × | 1 | × | 20 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | s | × | 20 | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | − | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 20 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 18 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 18 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 18 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 18 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 18 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 58 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 58 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 58 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 58 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 58 | s | + | 2 |
| = | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 56 | s | + | 2 |
方程化为:
| | s | s | s | + | s | s | × | 20 | − | s | × | 1 | s | + | 56 | s | + | 2 | = | s | ( | s | + | 20 | ) | ( | s | − | 1 | ) |
去掉方程右边的括号:
| 方程右边 = | s | s | ( | s | − | 1 | ) | + | s | × | 20 | ( | s | − | 1 | ) |
方程的解为:
s≈0.455560 ,保留6位小数
有 1个解。
解方程的详细方法请参阅:《方程的解法》
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