总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 d(d+1)(d+3)+(d+2)(d+1)d = d(d+2)(d+3)+(d+1)(d+2)(d+3) 的解.
题型:方程
解:原方程:| | d | ( | d | + | 1 | ) | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
去掉方程左边的括号:
| 方程左边 = | d | d | ( | d | + | 3 | ) | + | d | × | 1 | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | ( | d | + | 3 | ) | + | ( | d | + | 2 | ) | ( | d | + | 1 | ) | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | d | × | 1 | × | 3 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | d | × | 3 | + | ( | d | + | 2 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 3 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 5 | d | + | d |
方程化为:
| | d | d | d | + | d | d | × | 3 | + | d | × | 1 | d | + | 5 | d | + | d | = | d | ( | d | + | 2 | ) | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
去掉方程右边的括号:
| 方程右边 = | d | d | ( | d | + | 3 | ) | + | d | × | 2 | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | ( | d | + | 3 | ) | + | ( | d | + | 1 | ) | ( | d | + | 2 | ) | ( | d | + | 3 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 2 | × | 3 |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | d | × | 6 | + | ( | d | + | 1 | ) |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 6 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 12 | d | + | d |
| = | d | d | d | + | d | d | × | 3 | + | d | × | 2 | d | + | 15 | d | + | d |
方程的解为:
d1≈-2.366025 ,保留6位小数
d2≈-0.633975 ,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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