总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 -5+-5/r【1-1/(1+r)*4】+{4/[1-1/(1+r)*21]}/(1+r)*30+35.5/(1+r)*50 = 0 的解.
题型:方程
解:原方程:| | - | 5 | − | 5 | ÷ | r | × | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 4 | ) | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | ÷ | ( | 1 | + | r | ) | × | 30 | + | 71 2 | ÷ | ( | 1 | + | r | ) | × | 50 | = | 0 |
| | - | 5 | r | − | 5 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 4 | ) | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | ÷ | ( | 1 | + | r | ) | × | 30 | r | + | 71 2 | ÷ | ( | 1 | + | r | ) | × | 50 | r | = | 0 |
去掉方程左边的一个括号:
| | - | 5 | r | − | 5 | × | 1 | + | 5 | × | 1 | ÷ | ( | 1 | + | r | ) | × | 4 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | ÷ | ( | 1 | + | r | ) | × | 30 | r | = | 0 |
方程化简为:
| | - | 5 | r | − | 5 | + | 20 | ÷ | ( | 1 | + | r | ) | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | ÷ | ( | 1 | + | r | ) | × | 30 | r | + | 1775 | ÷ | ( | 1 | + | r | ) | × | r | = | 0 |
| | - | 5 | r | ( | 1 | + | r | ) | − | 5 | ( | 1 | + | r | ) | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | + | 1775 | r | = | 0 |
去掉方程左边的一个括号:
| | - | 5 | r | × | 1 | − | 5 | r | r | − | 5 | ( | 1 | + | r | ) | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | = | 0 |
方程化简为:
| | - | 5 | r | − | 5 | r | r | − | 5 | ( | 1 | + | r | ) | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | + | 1775 | = | 0 |
方程化简为:
| | 1770 | r | − | 5 | r | r | − | 5 | ( | 1 | + | r | ) | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | = | 0 |
去掉方程左边的一个括号:
| | 1770 | r | − | 5 | r | r | − | 5 | × | 1 | − | 5 | r | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | = | 0 |
方程化简为:
| | 1770 | r | − | 5 | r | r | − | 5 | − | 5 | r | + | 20 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | = | 0 |
方程化简为:
| | 1765 | r | − | 5 | r | r | + | 15 | + | ( | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ) | × | 30 | r | = | 0 |
去掉方程左边的一个括号:
| | 1765 | r | − | 5 | r | r | + | 15 | + | 4 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | × | 30 | r | = | 0 |
方程化简为:
| | 1765 | r | − | 5 | r | r | + | 15 | + | 120 | ÷ | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | × | r | = | 0 |
| 方程两边同时乘以: | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) |
| | 1765 | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | + | 15 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | + | 120 | r | = | 0 |
去掉方程左边的一个括号:
| | 1765 | r | × | 1 | − | 1765 | r | × | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | = | 0 |
方程化简为:
| | 1765 | r | − | 37065 | r | ÷ | ( | 1 | + | r | ) | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | + | 15 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | + | 120 | = | 0 |
方程化简为:
| | 1885 | r | − | 37065 | r | ÷ | ( | 1 | + | r | ) | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | + | 15 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | = | 0 |
| | 1885 | r | ( | 1 | + | r | ) | − | 37065 | r | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ( | 1 | + | r | ) | + | 15 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | = | 0 |
去掉方程左边的一个括号:
| | 1885 | r | × | 1 | + | 1885 | r | r | − | 37065 | r | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | = | 0 |
方程化简为:
| | 1885 | r | + | 1885 | r | r | − | 37065 | r | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ( | 1 | + | r | ) | = | 0 |
方程化简为:
| | - | 35180 | r | + | 1885 | r | r | − | 5 | r | r | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | ( | 1 | + | r | ) | + | 15 | ( | 1 | − | 1 | ÷ | ( | 1 | + | r | ) | × | 21 | ) | = | 0 |
去掉方程左边的一个括号:
| | - | 35180 | r | + | 1885 | r | r | − | 5 | r | r | × | 1 | ( | 1 | + | r | ) | + | 5 | r | = | 0 |
方程化简为:
| | - | 35180 | r | + | 1885 | r | r | − | 5 | r | r | ( | 1 | + | r | ) | + | 105 | r | r | = | 0 |
r≈18.594405 ,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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