总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 [1+(k*k)]*{[12-8(k*k)]/{[1-2(k*k)]*[1-2(k*k)]}} = 60 的解.
题型:方程
解:原方程:| | ( | 1 | + | ( | k | k | ) | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | = | 60 |
去掉方程左边的一个括号:
| | 1 | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | = | 60 |
去掉方程左边的一个括号:
| | 1 | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | = | 60 |
| 方程两边同时乘以: | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
| | 1 | ( | 12 | − | 8 | ( | k | k | ) | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程左边的一个括号:
| | 1 | × | 12 | − | 1 | × | 8 | ( | k | k | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程右边的一个括号:
| | 1 | × | 12 | − | 1 | × | 8 | ( | k | k | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
方程化简为:
| | 12 | − | 8 | ( | k | k | ) | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程左边的一个括号:
| | 12 | − | 8 | k | k | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程右边的一个括号:
| | 12 | − | 8 | k | k | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | × | 1 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 60 | × | 2 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
方程化简为:
| | 12 | − | 8 | k | k | + | ( | k | k | ) | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程左边的一个括号:
| | 12 | − | 8 | k | k | + | k | k | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程右边的一个括号:
| | 12 | − | 8 | k | k | + | k | k | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | × | 1 | − | 60 | × | 2 | ( | k | k | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
方程化简为:
| | 12 | − | 8 | k | k | + | k | k | ( | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | − | 120 | ( | k | k | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程左边的一个括号:
| | 12 | − | 8 | k | k | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | × | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | − | 120 | ( | k | k | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程右边的一个括号:
| | 12 | − | 8 | k | k | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | ÷ | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | × | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | − | 120 | k | k | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
| 方程两边同时乘以: | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
| | 12 | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程左边的一个括号:
| | 12 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程右边的一个括号:
| | 12 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程左边的一个括号:
| | 12 | × | 1 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 12 | × | 2 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
去掉方程右边的一个括号:
| | 12 | × | 1 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 12 | × | 2 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | = | 60 | × | 1 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 60 | × | 2 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 |
方程化简为:
| | 12 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 24 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | k | ( | 12 | − | 8 | ( | k | k | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程左边的一个括号:
| | 12 | × | 1 | − | 12 | × | 2 | ( | k | k | ) | − | 24 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) |
去掉方程右边的一个括号:
| | 12 | × | 1 | − | 12 | × | 2 | ( | k | k | ) | − | 24 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | = | 60 | × | 1 | − | 60 | × | 2 | ( | k | k | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) |
方程化简为:
| | 12 | − | 24 | ( | k | k | ) | − | 24 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 8 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | + | k | k | = | 60 | − | 120 | ( | k | k | ) | − | 120 | ( | k | k | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | − | 120 | k | k | ( | ( | 1 | − | 2 | ( | k | k | ) | ) | ( | 1 | − | 2 | ( | k | k | ) | ) | ) | − | 120 | ( | k | k | ) |
方程的解为:
k1≈-0.843833 ,保留6位小数
k2≈-0.521361 ,保留6位小数
k3≈0.521361 ,保留6位小数
k4≈0.843833 ,保留6位小数
有 4个解。
解程的详细方法请参阅:《方程的解法》
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