总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 50+40*(1+x)*(1+x)+20*(1+x)*(1+x)*(1+x) = 81*(1+x)*(1+x)*(1+x)*(1+x)*(1+x) 的解.
题型:方程
解:原方程:| | 50 | + | 40 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 81 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
去掉方程左边的括号:
| 方程左边 = | 50 | + | 40 | × | 1 | ( | 1 | + | x | ) | + | 40 | x | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 50 | + | 40 | ( | 1 | + | x | ) | + | 40 | x | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 50 | + | 40 | × | 1 | + | 40 | x | + | 40 | x | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 50 | + | 40 | + | 40 | x | + | 40 | x | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 90 | + | 40 | x | + | 40 | x | ( | 1 | + | x | ) | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 90 | + | 40 | x | + | 40 | x | × | 1 | + | 40 | x | x | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 90 | + | 40 | x | + | 40 | x | + | 40 | x | x | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | ( | 1 | + | x | ) |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | × | 1 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 20 | x |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | ( | 1 | + | x | ) | ( | 1 | + | x | ) | + | 20 | x | ( | 1 | + | x | ) |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | × | 1 | ( | 1 | + | x | ) | + | 20 | x | ( | 1 | + | x | ) |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | ( | 1 | + | x | ) | + | 20 | x | ( | 1 | + | x | ) | + | 20 |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | × | 1 | + | 20 | x | + | 20 | x |
| = | 90 | + | 80 | x | + | 40 | x | x | + | 20 | + | 20 | x | + | 20 | x | ( | 1 | + | x | ) |
| = | 110 | + | 100 | x | + | 40 | x | x | + | 20 | x | ( | 1 | + | x | ) | + | 20 | x | ( | 1 | + | x | ) |
| = | 110 | + | 100 | x | + | 40 | x | x | + | 20 | x | × | 1 | + | 20 | x | x |
| = | 110 | + | 100 | x | + | 40 | x | x | + | 20 | x | + | 20 | x | x | + | 20 |
| = | 110 | + | 120 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | ( | 1 | + | x | ) |
| = | 110 | + | 120 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | × | 1 |
| = | 110 | + | 120 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | ( | 1 | + | x | ) |
| = | 110 | + | 120 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | × | 1 |
| = | 110 | + | 120 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | + | 20 |
| = | 110 | + | 140 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | x |
| = | 110 | + | 140 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | x |
| = | 110 | + | 140 | x | + | 40 | x | x | + | 20 | x | x | + | 20 | x | x |
x≈0.087067 ,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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