总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 2100(1+x)+2100(1+x)(1+2x)*11+700(1+2x)*12 = 1.875*21700 的解.
题型:方程
解:原方程:| | 2100 | ( | 1 | + | x | ) | + | 2100 | ( | 1 | + | x | ) | ( | 1 | + | 2 | x | ) | × | 11 | + | 700 | ( | 1 | + | 2 | x | ) | × | 12 | = | 15 8 | × | 21700 |
| 方程左边 = | 2100 | ( | 1 | + | x | ) | + | 23100 | ( | 1 | + | x | ) | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
方程化为:
| | 2100 | ( | 1 | + | x | ) | + | 23100 | ( | 1 | + | x | ) | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) | = | 15 8 | × | 21700 |
去掉方程左边的括号:
| 方程左边 = | 2100 | × | 1 | + | 2100 | x | + | 23100 | ( | 1 | + | x | ) | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 2100 | + | 2100 | x | + | 23100 | ( | 1 | + | x | ) | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 2100 | + | 2100 | x | + | 23100 | × | 1 | ( | 1 | + | 2 | x | ) | + | 23100 | x | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 2100 | + | 2100 | x | + | 23100 | ( | 1 | + | 2 | x | ) | + | 23100 | x | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 2100 | + | 2100 | x | + | 23100 | × | 1 | + | 23100 | × | 2 | x | + | 23100 | x | ( | 1 | + | 2 | x | ) | + | 8400 |
| = | 2100 | + | 2100 | x | + | 23100 | + | 46200 | x | + | 23100 | x | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 25200 | + | 48300 | x | + | 23100 | x | ( | 1 | + | 2 | x | ) | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 25200 | + | 48300 | x | + | 23100 | x | × | 1 | + | 23100 | x | × | 2 | x | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 25200 | + | 48300 | x | + | 23100 | x | + | 46200 | x | x | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 25200 | + | 71400 | x | + | 46200 | x | x | + | 8400 | ( | 1 | + | 2 | x | ) |
| = | 25200 | + | 71400 | x | + | 46200 | x | x | + | 8400 | × | 1 | + | 8400 | × | 2 | x |
| = | 25200 | + | 71400 | x | + | 46200 | x | x | + | 8400 | + | 16800 | x |
| = | 33600 | + | 88200 | x | + | 46200 | x | x |
方程化为:
| | 33600 | + | 88200 | x | + | 46200 | x | x | = | 15 8 | × | 21700 |
方程化为:
| | 33600 | + | 88200 | x | + | 46200 | x | x | = | 81375 2 |
方程的解为:
x1≈-1.986324 ,保留6位小数
x2≈0.077233 ,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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