总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 40*(12+x)-40*17+x((13-x)*(-12-x)+17*8)-5((13-x)*(-8)+64) = 0 的解.
题型:方程
解:原方程:| | 40 | ( | 12 | + | x | ) | − | 40 | × | 17 | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) | = | 0 |
| 方程左边 = | 40 | ( | 12 | + | x | ) | − | 680 | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
方程化为:
| | 40 | ( | 12 | + | x | ) | − | 680 | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | 40 | × | 12 | + | 40 | x | − | 680 | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | 480 | + | 40 | x | − | 680 | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 40 | x | + | x | ( | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | 17 | × | 8 | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 40 | x | + | x | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | x | × | 17 | × | 8 | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 40 | x | + | x | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | + | x | × | 136 | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 176 | x | + | x | ( | 13 | − | x | ) | ( | - | 12 | − | x | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 176 | x | + | x | × | 13 | ( | - | 12 | − | x | ) | − | x | x | ( | - | 12 | − | x | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 176 | x | − | x | × | 13 | × | 12 | − | x | × | 13 | x | − | x | x | ( | - | 12 | − | x | ) |
| = | - | 200 | + | 176 | x | − | x | × | 156 | − | x | × | 13 | x | − | x | x | ( | - | 12 | − | x | ) | − | 5 |
| = | - | 200 | + | 20 | x | − | x | × | 13 | x | − | x | x | ( | - | 12 | − | x | ) | − | 5 | ( | ( | 13 | − | x | ) | ( | - | 8 | ) | + | 64 | ) |
| = | - | 200 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 200 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 200 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 520 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 520 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 520 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 520 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 520 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | - | 0 | + | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
| = | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x | − | 5 |
| = | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x | − | 40 |
| = | - | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x |
方程化为:
| | - | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x | = | 0 |
方程可以化为:
| | - | 20 | x | − | x | × | 13 | x | + | x | x | × | 12 | + | x | x | x | = | 0 |
x≈5.683905 ,保留6位小数
有 1个解。
解一元一次方程的详细方法请参阅:《一元一次方程的解法》
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