总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 952 = 100÷(1+r)+100÷((1+r)×(1+r))+1100÷((1+r)×(1+r)×(1+r)) 的解.
题型:方程
解:原方程: | 952 | = | 100 | ÷ | ( | 1 | + | r | ) | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
| 952 | ( | 1 | + | r | ) | = | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
去掉方程左边的一个括号:
| 952 | × | 1 | + | 952 | r | = | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
去掉方程右边的一个括号:
| 952 | × | 1 | + | 952 | r | = | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | 1 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | r | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
方程化简为:
| 952 | + | 952 | r | = | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | r | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
方程两边同时乘以: | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
| 952 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程左边的一个括号:
| 952 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程右边的一个括号:
| 952 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | + | 100 | + | 100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
方程两边同时乘以: | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
| 952 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
去掉方程左边的一个括号:
| 952 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 1100 | ÷ | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | × | ( | 1 | + | r | ) |
去掉方程右边的一个括号:
| 952 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r |
方程化简为:
| 952 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
方程两边同时乘以: | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
| 952 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程左边的一个括号:
| 952 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程右边的一个括号:
| 952 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
方程化简为:
| 952 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程左边的一个括号:
| 952 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程右边的一个括号:
| 952 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程左边的一个括号:
| 952 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
去掉方程右边的一个括号:
| 952 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | = | 100 | × | 1 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) |
方程化简为:
| 952 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | = | 100 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 |
去掉方程左边的一个括号:
| 952 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | = | 100 | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 |
去掉方程右边的一个括号:
| 952 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 952 | r | = | 100 | × | 1 | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r | ( | 1 | + | r | ) | ( | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ( | 1 | + | r | ) | ) | + | 100 | r |
r≈0.119984 ,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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