总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (100-x)(50-x)(-10-x)-24000-24000-400(50-x)-1600(-10-x)-900(100-x) = 0 的解.
题型:方程
解:原方程:| | ( | 100 | − | x | ) | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 24000 | − | 24000 | − | 400 | ( | 50 | − | x | ) | − | 1600 | ( | - | 10 | − | x | ) | − | 900 | ( | 100 | − | x | ) | = | 0 |
| 方程左边 = | ( | 100 | − | x | ) | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) | − | 1600 | ( | - | 10 | − | x | ) | − | 900 | ( | 100 | − | x | ) |
方程化为:
| | ( | 100 | − | x | ) | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) | − | 1600 | ( | - | 10 | − | x | ) | − | 900 | ( | 100 | − | x | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | 100 | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) | − | 1600 | ( | - | 10 | − | x | ) | − | 900 |
| = | 100 | × | 50 | ( | - | 10 | − | x | ) | − | 100 | x | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) |
| = | 5000 | ( | - | 10 | − | x | ) | − | 100 | x | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) | − | 1600 |
| = | - | 5000 | × | 10 | − | 5000 | x | − | 100 | x | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 |
| = | - | 50000 | − | 5000 | x | − | 100 | x | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 48000 | − | 400 | ( | 50 | − | x | ) |
| = | - | 98000 | − | 5000 | x | − | 100 | x | ( | - | 10 | − | x | ) | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 400 | ( | 50 | − | x | ) | − | 1600 |
| = | - | 98000 | − | 5000 | x | + | 100 | x | × | 10 | + | 100 | x | x | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) |
| = | - | 98000 | − | 5000 | x | + | 1000 | x | + | 100 | x | x | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 400 |
| = | - | 98000 | − | 4000 | x | + | 100 | x | x | − | x | ( | 50 | − | x | ) | ( | - | 10 | − | x | ) | − | 400 | ( | 50 | − | x | ) | − | 1600 |
| = | - | 98000 | − | 4000 | x | + | 100 | x | x | − | x | × | 50 | ( | - | 10 | − | x | ) | + | x | x | ( | - | 10 | − | x | ) |
| = | - | 98000 | − | 4000 | x | + | 100 | x | x | + | x | × | 50 | × | 10 | + | x | × | 50 | x |
| = | - | 98000 | − | 4000 | x | + | 100 | x | x | + | x | × | 500 | + | x | × | 50 | x | + | x |
| = | - | 98000 | − | 3500 | x | + | 100 | x | x | + | x | × | 50 | x | + | x | x | ( | - | 10 | − | x | ) |
| = | - | 98000 | − | 3500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 98000 | − | 3500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 98000 | − | 3500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 118000 | − | 3100 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 118000 | − | 3100 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 118000 | − | 3100 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 102000 | − | 1500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 102000 | − | 1500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 102000 | − | 1500 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
| = | - | 192000 | − | 600 | x | + | 100 | x | x | + | x | × | 50 | x | − | x | x | × | 10 |
方程的解为:
x1≈-31.735234 ,保留6位小数
x2≈49.491941 ,保留6位小数
x3≈122.243293 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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