总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (30-20x)×(18-15x)×(6-10x)-36×(30-20x)+144×(10x-6) = 0 的解.
题型:方程
解:原方程:| | ( | 30 | − | 20 | x | ) | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 | ( | 30 | − | 20 | x | ) | + | 144 | ( | 10 | x | − | 6 | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | 30 | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 | ( | 30 | − | 20 | x | ) | + | 144 | ( | 10 | x | − | 6 | ) |
| = | 30 | × | 18 | ( | 6 | − | 10 | x | ) | − | 30 | × | 15 | x | ( | 6 | − | 10 | x | ) | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 |
| = | 540 | ( | 6 | − | 10 | x | ) | − | 450 | x | ( | 6 | − | 10 | x | ) | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 | ( | 30 | − | 20 | x | ) | + | 144 |
| = | 540 | × | 6 | − | 540 | × | 10 | x | − | 450 | x | ( | 6 | − | 10 | x | ) | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) |
| = | 3240 | − | 5400 | x | − | 450 | x | ( | 6 | − | 10 | x | ) | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 | ( | 30 | − | 20 | x | ) |
| = | 3240 | − | 5400 | x | − | 450 | x | × | 6 | + | 450 | x | × | 10 | x | − | 20 | x |
| = | 3240 | − | 5400 | x | − | 2700 | x | + | 4500 | x | x | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) |
| = | 3240 | − | 8100 | x | + | 4500 | x | x | − | 20 | x | ( | 18 | − | 15 | x | ) | ( | 6 | − | 10 | x | ) | − | 36 | ( | 30 | − | 20 | x | ) |
| = | 3240 | − | 8100 | x | + | 4500 | x | x | − | 20 | x | × | 18 | ( | 6 | − | 10 | x | ) | + | 20 | x |
| = | 3240 | − | 8100 | x | + | 4500 | x | x | − | 360 | x | ( | 6 | − | 10 | x | ) | + | 300 | x | x |
| = | 3240 | − | 8100 | x | + | 4500 | x | x | − | 360 | x | × | 6 | + | 360 | x | × | 10 |
| = | 3240 | − | 8100 | x | + | 4500 | x | x | − | 2160 | x | + | 3600 | x | x | + | 300 |
| = | 3240 | − | 10260 | x | + | 4500 | x | x | + | 3600 | x | x | + | 300 | x | x |
| = | 3240 | − | 10260 | x | + | 4500 | x | x | + | 3600 | x | x | + | 300 | x | x |
| = | 3240 | − | 10260 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 3240 | − | 10260 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 3240 | − | 10260 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 2160 | − | 9540 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 2160 | − | 9540 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 2160 | − | 9540 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
| = | 1296 | − | 8100 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x |
方程化为:
| | 1296 | − | 8100 | x | + | 4500 | x | x | + | 3600 | x | x | + | 1800 | x | x | = | 0 |
方程的解为:
x1≈0.210879 ,保留6位小数
x2≈0.963959 ,保留6位小数
x3≈2.125162 ,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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