总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 950 = 700/(1+x)+550/(1+x)/(1+x)+130/(1+x)/(1+x)/(1+x) 的解.
题型:方程
解:原方程:| | 950 | = | 700 | ÷ | ( | 1 | + | x | ) | + | 550 | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) | + | 130 | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) |
| | 950 | ( | 1 | + | x | ) | = | 700 | + | 550 | ÷ | ( | 1 | + | x | ) | + | 130 | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) |
去掉方程左边的一个括号:
| | 950 | × | 1 | + | 950 | x | = | 700 | + | 550 | ÷ | ( | 1 | + | x | ) | + | 130 | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) |
方程化简为:
| | 950 | + | 950 | x | = | 700 | + | 550 | ÷ | ( | 1 | + | x | ) | + | 130 | ÷ | ( | 1 | + | x | ) | ÷ | ( | 1 | + | x | ) |
| | 950 | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | = | 700 | ( | 1 | + | x | ) | + | 550 | + | 130 | ÷ | ( | 1 | + | x | ) |
去掉方程左边的一个括号:
| | 950 | × | 1 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | = | 700 | ( | 1 | + | x | ) | + | 550 | + | 130 | ÷ | ( | 1 | + | x | ) |
去掉方程右边的一个括号:
| | 950 | × | 1 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | = | 700 | × | 1 | + | 700 | x | + | 550 | + | 130 | ÷ | ( | 1 | + | x | ) |
方程化简为:
| | 950 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | = | 700 | + | 700 | x | + | 550 | + | 130 | ÷ | ( | 1 | + | x | ) |
方程化简为:
| | 950 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | = | 1250 | + | 700 | x | + | 130 | ÷ | ( | 1 | + | x | ) |
| | 950 | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1250 | ( | 1 | + | x | ) | + | 700 | x | ( | 1 | + | x | ) | + | 130 |
去掉方程左边的一个括号:
| | 950 | × | 1 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1250 | ( | 1 | + | x | ) | + | 700 | x | ( | 1 | + | x | ) | + | 130 |
去掉方程右边的一个括号:
| | 950 | × | 1 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1250 | × | 1 | + | 1250 | x | + | 700 | x | ( | 1 | + | x | ) | + | 130 |
方程化简为:
| | 950 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1250 | + | 1250 | x | + | 700 | x | ( | 1 | + | x | ) | + | 130 |
方程化简为:
| | 950 | + | 950 | x | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1380 | + | 1250 | x | + | 700 | x | ( | 1 | + | x | ) |
去掉方程左边的一个括号:
| | 950 | + | 950 | x | + | 950 | x | × | 1 | + | 950 | x | x | + | 950 | x | ( | 1 | + | x | ) | = | 1380 | + | 1250 | x | + | 700 | x | ( | 1 | + | x | ) |
去掉方程右边的一个括号:
| | 950 | + | 950 | x | + | 950 | x | × | 1 | + | 950 | x | x | + | 950 | x | ( | 1 | + | x | ) | = | 1380 | + | 1250 | x | + | 700 | x | × | 1 | + | 700 | x | x |
方程化简为:
| | 950 | + | 950 | x | + | 950 | x | + | 950 | x | x | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1380 | + | 1250 | x | + | 700 | x | + | 700 | x | x |
方程化简为:
| | 950 | + | 1900 | x | + | 950 | x | x | + | 950 | x | ( | 1 | + | x | ) | ( | 1 | + | x | ) | = | 1380 | + | 1950 | x | + | 700 | x | x |
去掉方程左边的一个括号:
| | 950 | + | 1900 | x | + | 950 | x | x | + | 950 | x | × | 1 | ( | 1 | + | x | ) | + | 950 | x | = | 1380 | + | 1950 | x | + | 700 | x | x |
方程化简为:
| | 950 | + | 1900 | x | + | 950 | x | x | + | 950 | x | ( | 1 | + | x | ) | + | 950 | x | x | = | 1380 | + | 1950 | x | + | 700 | x | x |
去掉方程左边的一个括号:
| | 950 | + | 1900 | x | + | 950 | x | x | + | 950 | x | × | 1 | + | 950 | x | x | = | 1380 | + | 1950 | x | + | 700 | x | x |
方程化简为:
| | 950 | + | 1900 | x | + | 950 | x | x | + | 950 | x | + | 950 | x | x | + | 950 | = | 1380 | + | 1950 | x | + | 700 | x | x |
方程化简为:
| | 950 | + | 2850 | x | + | 950 | x | x | + | 950 | x | x | + | 950 | x | x | = | 1380 | + | 1950 | x | + | 700 | x | x |
去掉方程左边的一个括号:
| | 950 | + | 2850 | x | + | 950 | x | x | + | 950 | x | x | + | 950 | x | x | = | 1380 | + | 1950 | x | + | 700 | x | x |
x≈0.275065 ,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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