总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (6-2*x)*(6-6*x)*(5-2*x)-36-9*(6-2*x)-9*(5-2*x)-4*(6-6*x) = 0 的解.
题型:方程
解:原方程:| | ( | 6 | − | 2 | x | ) | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 36 | − | 9 | ( | 6 | − | 2 | x | ) | − | 9 | ( | 5 | − | 2 | x | ) | − | 4 | ( | 6 | − | 6 | x | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | 6 | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 36 | − | 9 | ( | 6 | − | 2 | x | ) | − | 9 | ( | 5 | − | 2 | x | ) |
| = | 6 | × | 6 | ( | 5 | − | 2 | x | ) | − | 6 | × | 6 | x | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 36 |
| = | 36 | ( | 5 | − | 2 | x | ) | − | 36 | x | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 36 | − | 9 | ( | 6 | − | 2 | x | ) |
| = | 36 | × | 5 | − | 36 | × | 2 | x | − | 36 | x | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) |
| = | 180 | − | 72 | x | − | 36 | x | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 36 | − | 9 |
| = | 144 | − | 72 | x | − | 36 | x | ( | 5 | − | 2 | x | ) | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 9 | ( | 6 | − | 2 | x | ) |
| = | 144 | − | 72 | x | − | 36 | x | × | 5 | + | 36 | x | × | 2 | x | − | 2 | x |
| = | 144 | − | 72 | x | − | 180 | x | + | 72 | x | x | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) |
| = | 144 | − | 252 | x | + | 72 | x | x | − | 2 | x | ( | 6 | − | 6 | x | ) | ( | 5 | − | 2 | x | ) | − | 9 | ( | 6 | − | 2 | x | ) |
| = | 144 | − | 252 | x | + | 72 | x | x | − | 2 | x | × | 6 | ( | 5 | − | 2 | x | ) | + | 2 | x |
| = | 144 | − | 252 | x | + | 72 | x | x | − | 12 | x | ( | 5 | − | 2 | x | ) | + | 12 | x | x |
| = | 144 | − | 252 | x | + | 72 | x | x | − | 12 | x | × | 5 | + | 12 | x | × | 2 |
| = | 144 | − | 252 | x | + | 72 | x | x | − | 60 | x | + | 24 | x | x | + | 12 |
| = | 144 | − | 312 | x | + | 72 | x | x | + | 24 | x | x | + | 12 | x | x |
| = | 144 | − | 312 | x | + | 72 | x | x | + | 24 | x | x | + | 12 | x | x |
| = | 144 | − | 312 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 144 | − | 312 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 144 | − | 312 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 90 | − | 294 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 90 | − | 294 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 90 | − | 294 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 45 | − | 276 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 45 | − | 276 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 45 | − | 276 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
| = | 21 | − | 252 | x | + | 72 | x | x | + | 24 | x | x | + | 60 | x | x |
方程的解为:
x1≈0.088070 ,保留6位小数
x2≈2.620380 ,保留6位小数
x3≈3.791550 ,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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