总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 36*(50-2*x)+2*(2*x-10)*(50-2*x)*28+4*x(x-10)*36 = 48000 的解.
题型:方程
解:原方程:| | 36 | ( | 50 | − | 2 | x | ) | + | 2 | ( | 2 | x | − | 10 | ) | ( | 50 | − | 2 | x | ) | × | 28 | + | 4 | x | ( | x | − | 10 | ) | × | 36 | = | 48000 |
| 方程左边 = | 36 | ( | 50 | − | 2 | x | ) | + | 56 | ( | 2 | x | − | 10 | ) | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) |
方程化为:
| | 36 | ( | 50 | − | 2 | x | ) | + | 56 | ( | 2 | x | − | 10 | ) | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) | = | 48000 |
去掉方程左边的括号:
| 方程左边 = | 36 | × | 50 | − | 36 | × | 2 | x | + | 56 | ( | 2 | x | − | 10 | ) | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) |
| = | 1800 | − | 72 | x | + | 56 | ( | 2 | x | − | 10 | ) | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) |
| = | 1800 | − | 72 | x | + | 56 | × | 2 | x | ( | 50 | − | 2 | x | ) | − | 56 | × | 10 | ( | 50 | − | 2 | x | ) | + | 144 | x |
| = | 1800 | − | 72 | x | + | 112 | x | ( | 50 | − | 2 | x | ) | − | 560 | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) |
| = | 1800 | − | 72 | x | + | 112 | x | × | 50 | − | 112 | x | × | 2 | x | − | 560 | ( | 50 | − | 2 | x | ) |
| = | 1800 | − | 72 | x | + | 5600 | x | − | 224 | x | x | − | 560 | ( | 50 | − | 2 | x | ) | + | 144 | x |
| = | 1800 | + | 5528 | x | − | 224 | x | x | − | 560 | ( | 50 | − | 2 | x | ) | + | 144 | x | ( | x | − | 10 | ) |
| = | 1800 | + | 5528 | x | − | 224 | x | x | − | 560 | × | 50 | + | 560 | × | 2 | x | + | 144 |
| = | 1800 | + | 5528 | x | − | 224 | x | x | − | 28000 | + | 1120 | x | + | 144 | x | ( | x | − | 10 | ) |
| = | - | 26200 | + | 6648 | x | − | 224 | x | x | + | 144 | x | ( | x | − | 10 | ) |
| = | - | 26200 | + | 6648 | x | − | 224 | x | x | + | 144 | x | x | − | 144 | x | × | 10 |
| = | - | 26200 | + | 6648 | x | − | 224 | x | x | + | 144 | x | x | − | 1440 | x |
| = | - | 26200 | + | 5208 | x | − | 224 | x | x | + | 144 | x | x |
方程化为:
| | - | 26200 | + | 5208 | x | − | 224 | x | x | + | 144 | x | x | = | 48000 |
方程的解为:
x1≈21.060766 ,保留6位小数
x2≈44.039234 ,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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