总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 1/(d+10) = 1/d+1/(d+1)+1/(d+2) 的解.
题型:方程
解:原方程:| | 1 | ÷ | ( | d | + | 10 | ) | = | 1 | ÷ | d | + | 1 | ÷ | ( | d | + | 1 | ) | + | 1 | ÷ | ( | d | + | 2 | ) |
| | 1 | d | = | 1 | ( | d | + | 10 | ) | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
去掉方程右边的一个括号:
| | 1 | d | = | 1 | d | + | 1 | × | 10 | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
方程化简为:
| | 1 | d | = | 1 | d | + | 10 | + | 1 | ÷ | ( | d | + | 1 | ) | × | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
| | 1 | d | ( | d | + | 1 | ) | = | 1 | d | ( | d | + | 1 | ) | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
去掉方程左边的一个括号:
| | 1 | d | d | + | 1 | d | × | 1 | = | 1 | d | ( | d | + | 1 | ) | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) | × | ( | d | + | 10 | ) | d |
去掉方程右边的一个括号:
| | 1 | d | d | + | 1 | d | × | 1 | = | 1 | d | d | + | 1 | d | × | 1 | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 |
方程化简为:
| | 1 | d | d | + | 1 | d | = | 1 | d | d | + | 1 | d | + | 10 | ( | d | + | 1 | ) | + | 1 | ( | d | + | 10 | ) | d | + | 1 | ÷ | ( | d | + | 2 | ) |
| | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) | ( | d | + | 2 | ) | + | 1 | ( | d | + | 10 | ) |
去掉方程左边的一个括号:
| | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | ( | d | + | 2 | ) | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) | ( | d | + | 2 | ) | + | 1 | ( | d | + | 10 | ) |
去掉方程右边的一个括号:
| | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | d | + | 1 | d | d | × | 2 | + | 1 | d | ( | d | + | 2 | ) | + | 10 |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) |
去掉方程左边的一个括号:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | ( | d | + | 2 | ) | + | 10 | ( | d | + | 1 | ) |
去掉方程右边的一个括号:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 1 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
去掉方程右边的一个括号:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
去掉方程右边的一个括号:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
去掉方程右边的一个括号:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 22 | d |
方程化简为:
| | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 2 | d | = | 1 | d | d | d | + | 2 | d | d | + | 1 | d | d | + | 32 | d |
方程的解为:
d1≈-14.475218 ,保留6位小数
d2≈-1.590405 ,保留6位小数
d3≈-0.434377 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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