总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 4i*(1+i)*(1+i)*(1+i)*(1+i)*(1+i) = (1+i)*(1+i)*(1+i)*(1+i)*(1+i)-1 的解.
题型:方程
解:原方程:| | 4 | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | = | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | − | 1 |
去掉方程左边的括号:
| 方程左边 = | 4 | i | × | 1 | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) |
| = | 4 | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) |
| = | 4 | i | × | 1 | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) |
| = | 4 | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 |
| = | 4 | i | × | 1 | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i |
| = | 4 | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) | + | 4 | i | i |
| = | 4 | i | × | 1 | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) |
| = | 4 | i | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | + | 4 | i | i | ( | 1 | + | i | ) | ( | 1 | + | i | ) |
| = | 4 | i | × | 1 | + | 4 | i | i | + | 4 | i | i | ( | 1 | + | i | ) | + | 4 | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | ( | 1 | + | i | ) | + | 4 | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | × | 1 | + | 4 | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
| = | 4 | i | + | 4 | i | i | + | 4 | i | i | + | 4 | i | i | i |
方程化为一般式后,有公因式:
( i - 0 )
由
i - 0 = 0
得:
i1=0
不能由因式分解法得出的解:
i2≈0.079308 ,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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