总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 19600(1+2m)+2100(1+m)+19600*11(1+2m)+2100(1+2m)(1+m)*11 = 21700*1.875 的解.
题型:方程
解:原方程:| | 19600 | ( | 1 | + | 2 | m | ) | + | 2100 | ( | 1 | + | m | ) | + | 19600 | × | 11 | ( | 1 | + | 2 | m | ) | + | 2100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) | × | 11 | = | 21700 | × | 15 8 |
| 方程左边 = | 19600 | ( | 1 | + | 2 | m | ) | + | 2100 | ( | 1 | + | m | ) | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
方程化为:
| | 19600 | ( | 1 | + | 2 | m | ) | + | 2100 | ( | 1 | + | m | ) | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) | = | 21700 | × | 15 8 |
去掉方程左边的括号:
| 方程左边 = | 19600 | × | 1 | + | 19600 | × | 2 | m | + | 2100 | ( | 1 | + | m | ) | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 19600 | + | 39200 | m | + | 2100 | ( | 1 | + | m | ) | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 19600 | + | 39200 | m | + | 2100 | × | 1 | + | 2100 | m | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 19600 | + | 39200 | m | + | 2100 | + | 2100 | m | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 21700 | + | 41300 | m | + | 215600 | ( | 1 | + | 2 | m | ) | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 21700 | + | 41300 | m | + | 215600 | × | 1 | + | 215600 | × | 2 | m | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 21700 | + | 41300 | m | + | 215600 | + | 431200 | m | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 237300 | + | 472500 | m | + | 23100 | ( | 1 | + | 2 | m | ) | ( | 1 | + | m | ) |
| = | 237300 | + | 472500 | m | + | 23100 | × | 1 | ( | 1 | + | m | ) | + | 23100 | × | 2 | m | ( | 1 | + | m | ) |
| = | 237300 | + | 472500 | m | + | 23100 | ( | 1 | + | m | ) | + | 46200 | m | ( | 1 | + | m | ) |
| = | 237300 | + | 472500 | m | + | 23100 | × | 1 | + | 23100 | m | + | 46200 | m | ( | 1 | + | m | ) |
| = | 237300 | + | 472500 | m | + | 23100 | + | 23100 | m | + | 46200 | m | ( | 1 | + | m | ) |
| = | 260400 | + | 495600 | m | + | 46200 | m | ( | 1 | + | m | ) |
| = | 260400 | + | 495600 | m | + | 46200 | m | × | 1 | + | 46200 | m | m |
| = | 260400 | + | 495600 | m | + | 46200 | m | + | 46200 | m | m |
| = | 260400 | + | 541800 | m | + | 46200 | m | m |
方程化为:
| | 260400 | + | 541800 | m | + | 46200 | m | m | = | 21700 | × | 15 8 |
方程化为:
| | 260400 | + | 541800 | m | + | 46200 | m | m | = | 81375 2 |
方程的解为:
m1≈-11.306664 ,保留6位小数
m2≈-0.420609 ,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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