总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (10x+1)(10x+1)(10x+1)(10x+1)(10x+1)-(40x+1)(40x+1) = 0 的解.
题型:方程
解:原方程:| | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | − | ( | 40 | x | + | 1 | ) | ( | 40 | x | + | 1 | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | 10 | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 1 | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | − | ( | 40 | x | + | 1 | ) |
| = | 10 | x | × | 10 | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 10 | x | × | 1 | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) |
| = | 100 | x | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 10 | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 1 |
| = | 100 | x | x | × | 10 | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 100 | x | x | × | 1 | ( | 10 | x | + | 1 | ) |
| = | 1000 | x | x | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 100 | x | x | ( | 10 | x | + | 1 | ) | ( | 10 | x | + | 1 | ) | + | 10 |
| = | 1000 | x | x | x | × | 10 | x | ( | 10 | x | + | 1 | ) | + | 1000 | x | x | x | × | 1 |
| = | 10000 | x | x | x | x | ( | 10 | x | + | 1 | ) | + | 1000 | x | x | x | ( | 10 | x | + | 1 | ) | + | 100 |
| = | 10000 | x | x | x | x | × | 10 | x | + | 10000 | x | x | x | x |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 1000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 1000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
| = | 100000 | x | x | x | x | x | + | 10000 | x | x | x | x | + | 10000 |
x≈0.072006 ,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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