总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 [(50+3x)(40+2x)-40*50]*30+(50+3x)(40+2x)*100 = 642000 的解.
题型:方程
解:原方程:| | ( | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | − | 40 | × | 50 | ) | × | 30 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 | = | 642000 |
去掉方程左边的括号:
| 方程左边 = | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 30 | − | 40 | × | 50 | × | 30 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 30 | − | 60000 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 50 | ( | 40 | + | 2 | x | ) | × | 30 | + | 3 | x | ( | 40 | + | 2 | x | ) | × | 30 | − | 60000 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 1500 | ( | 40 | + | 2 | x | ) | + | 90 | x | ( | 40 | + | 2 | x | ) | − | 60000 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 1500 | × | 40 | + | 1500 | × | 2 | x | + | 90 | x | ( | 40 | + | 2 | x | ) | − | 60000 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 60000 | + | 3000 | x | + | 90 | x | ( | 40 | + | 2 | x | ) | − | 60000 | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 0 | + | 3000 | x | + | 90 | x | ( | 40 | + | 2 | x | ) | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 3000 | x | + | 90 | x | × | 40 | + | 90 | x | × | 2 | x | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 3000 | x | + | 3600 | x | + | 180 | x | x | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 6600 | x | + | 180 | x | x | + | ( | 50 | + | 3 | x | ) | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 6600 | x | + | 180 | x | x | + | 50 | ( | 40 | + | 2 | x | ) | × | 100 | + | 3 | x | ( | 40 | + | 2 | x | ) | × | 100 |
| = | 6600 | x | + | 180 | x | x | + | 5000 | ( | 40 | + | 2 | x | ) | + | 300 | x | ( | 40 | + | 2 | x | ) |
| = | 6600 | x | + | 180 | x | x | + | 5000 | × | 40 | + | 5000 | × | 2 | x | + | 300 | x |
| = | 6600 | x | + | 180 | x | x | + | 200000 | + | 10000 | x | + | 300 | x | ( | 40 | + | 2 | x | ) |
| = | 16600 | x | + | 180 | x | x | + | 200000 | + | 300 | x | ( | 40 | + | 2 | x | ) |
| = | 16600 | x | + | 180 | x | x | + | 200000 | + | 300 | x | × | 40 | + | 300 | x | × | 2 |
| = | 16600 | x | + | 180 | x | x | + | 200000 | + | 12000 | x | + | 600 | x | x |
| = | 28600 | x | + | 180 | x | x | + | 200000 | + | 600 | x | x |
方程化为:
| | 28600 | x | + | 180 | x | x | + | 200000 | + | 600 | x | x | = | 642000 |
方程的解为:
x1≈-48.379594 ,保留6位小数
x2≈11.712927 ,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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