总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 80*200+(80-x)(200+10x)+40*(800-200-(200+10x))-50*800 = 7500 的解.
题型:方程
解:原方程:| | 80 | × | 200 | + | ( | 80 | − | x | ) | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) | − | 50 | × | 800 | = | 7500 |
| 方程左边 = | 16000 | + | ( | 80 | − | x | ) | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) | − | 40000 |
| = | - | 24000 | + | ( | 80 | − | x | ) | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
方程化为:
| | - | 24000 | + | ( | 80 | − | x | ) | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) | = | 7500 |
去掉方程左边的括号:
| 方程左边 = | - | 24000 | + | 80 | ( | 200 | + | 10 | x | ) | − | x | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 24000 | + | 80 | × | 200 | + | 80 | × | 10 | x | − | x | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 24000 | + | 16000 | + | 800 | x | − | x | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 8000 | + | 800 | x | − | x | ( | 200 | + | 10 | x | ) | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 8000 | + | 800 | x | − | x | × | 200 | − | x | × | 10 | x | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 8000 | + | 600 | x | − | x | × | 10 | x | + | 40 | ( | 800 | − | 200 | − | ( | 200 | + | 10 | x | ) | ) |
| = | - | 8000 | + | 600 | x | − | x | × | 10 | x | + | 40 | × | 800 | − | 40 | × | 200 | − | 40 | ( | 200 | + | 10 | x | ) |
| = | - | 8000 | + | 600 | x | − | x | × | 10 | x | + | 32000 | − | 8000 | − | 40 | ( | 200 | + | 10 | x | ) |
| = | 16000 | + | 600 | x | − | x | × | 10 | x | − | 40 | ( | 200 | + | 10 | x | ) |
| = | 16000 | + | 600 | x | − | x | × | 10 | x | − | 40 | × | 200 | − | 40 | × | 10 | x |
| = | 16000 | + | 600 | x | − | x | × | 10 | x | − | 8000 | − | 400 | x |
| = | 8000 | + | 200 | x | − | x | × | 10 | x |
方程化为:
| | 8000 | + | 200 | x | − | x | × | 10 | x | = | 7500 |
方程的解为:
x1≈-2.247449 ,保留6位小数
x2≈22.247449 ,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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