总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (s+1)(s+4)s = (s+2)((s+1)(s+4)+s(s+4)+s(s+1)) 的解.
题型:方程
解:原方程:| | ( | s | + | 1 | ) | ( | s | + | 4 | ) | s | = | ( | s | + | 2 | ) | ( | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | ( | s | + | 4 | ) | + | s | ( | s | + | 1 | ) | ) |
去掉方程左边的括号:
| 方程左边 = | s | ( | s | + | 4 | ) | s | + | 1 | ( | s | + | 4 | ) | s |
| = | s | s | s | + | s | × | 4 | s | + | 1 | ( | s | + | 4 | ) | s |
| = | s | s | s | + | s | × | 4 | s | + | 1 | s | s | + | 1 | × | 4 | s |
| = | s | s | s | + | s | × | 4 | s | + | 1 | s | s | + | 4 | s |
方程化为:
| | s | s | s | + | s | × | 4 | s | + | 1 | s | s | + | 4 | s | = | ( | s | + | 2 | ) | ( | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | ( | s | + | 4 | ) | + | s | ( | s | + | 1 | ) | ) |
去掉方程右边的括号:
| 方程右边 = | s | ( | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | ( | s | + | 4 | ) | + | s | ( | s | + | 1 | ) | ) | + | 2 | ( | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | ( | s | + | 4 | ) | + | s | ( | s | + | 1 | ) | ) |
| = | s | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | s | ( | s | + | 4 | ) | + | s | s | ( | s | + | 1 | ) | + | 2 | ( | ( | s | + | 1 | ) | ( | s | + | 4 | ) | + | s | ( | s | + | 4 | ) | + | s | ( | s | + | 1 | ) | ) |
| = | s | s | ( | s | + | 4 | ) | + | s | × | 1 | ( | s | + | 4 | ) | + | s | s | ( | s | + | 4 | ) | + | s | s | ( | s | + | 1 | ) |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | ( | s | + | 4 | ) | + | s | s | ( | s | + | 4 | ) |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | s | × | 1 | × | 4 |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | s | × | 4 | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 4 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 12 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 12 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 12 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 14 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 14 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 14 | s | + | s |
| = | s | s | s | + | s | s | × | 4 | + | s | × | 1 | s | + | 22 | s | + | s |
方程的解为:
s≈-0.549460 ,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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