总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (1+x)*(1+x)*(1+x)*(1+x)*(1+x)*(1+x)*(1+x)*(1+x)*(1+x)*(1+x)*23656 = 27592 的解.
题型:方程
解:原方程:| | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | × | 23656 | = | 27592 |
去掉方程左边的括号:
| 方程左边 = | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | × | 23656 | + | x |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | x | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) |
| = | 23656 | × | 1 | + | 23656 | x | + | 23656 | x | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 |
| = | 23656 | + | 23656 | x | + | 23656 | x | ( | 1 | + | x | ) | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | + | 23656 | x | + | 23656 | x | × | 1 | + | 23656 | x | x | + | 23656 | x | ( | 1 | + | x | ) |
| = | 23656 | + | 23656 | x | + | 23656 | x | + | 23656 | x | x | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 23656 | + | 47312 | x | + | 23656 | x | x | + | 23656 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | + | 47312 | x | + | 23656 | x | x | + | 23656 | x | × | 1 | ( | 1 | + | x | ) | + | 23656 | x |
| = | 23656 | + | 47312 | x | + | 23656 | x | x | + | 23656 | x | ( | 1 | + | x | ) | + | 23656 | x | x |
方程的解为:
x1≈-2.015510 ,保留6位小数
x2≈0.015510 ,保留6位小数
有 2个解。
解程的详细方法请参阅:《方程的解法》
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