总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 77831*(1+x)+77831*(1+x)*(1+x)+77831*(1+x)*(1+x)*(1+x) = 132313 的解.
题型:方程
解:原方程:| | 77831 | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 132313 |
去掉方程左边的括号:
| 方程左边 = | 77831 | × | 1 | + | 77831 | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 77831 | + | 77831 | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 77831 | + | 77831 | x | + | 77831 | × | 1 | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 77831 | + | 77831 | x | + | 77831 | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 77831 | + | 77831 | x | + | 77831 | × | 1 | + | 77831 | x | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) |
| = | 77831 | + | 77831 | x | + | 77831 | + | 77831 | x | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 155662 | + | 155662 | x | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 155662 | + | 155662 | x | + | 77831 | x | × | 1 | + | 77831 | x | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 155662 | + | 155662 | x | + | 77831 | x | + | 77831 | x | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 77831 | x |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | × | 1 | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | × | 1 | + | 77831 | x | + | 77831 | x |
| = | 155662 | + | 233493 | x | + | 77831 | x | x | + | 77831 | + | 77831 | x | + | 77831 | x | ( | 1 | + | x | ) |
| = | 233493 | + | 311324 | x | + | 77831 | x | x | + | 77831 | x | ( | 1 | + | x | ) | + | 77831 | x | ( | 1 | + | x | ) |
| = | 233493 | + | 311324 | x | + | 77831 | x | x | + | 77831 | x | × | 1 | + | 77831 | x | x |
| = | 233493 | + | 311324 | x | + | 77831 | x | x | + | 77831 | x | + | 77831 | x | x | + | 77831 |
| = | 233493 | + | 389155 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | ( | 1 | + | x | ) |
| = | 233493 | + | 389155 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | × | 1 |
| = | 233493 | + | 389155 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | ( | 1 | + | x | ) |
| = | 233493 | + | 389155 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | × | 1 |
| = | 233493 | + | 389155 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | + | 77831 |
| = | 233493 | + | 466986 | x | + | 77831 | x | x | + | 77831 | x | x | + | 77831 | x | x |
x≈-0.258261 ,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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