总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 {[(2k+2)(2k+2)]/k2+1*[(1+k)*(1+k)]*[(4k/3-k2)*(4k/3-k2)]}+28/(3-k2) = 1440 的解.
题型:方程
解:原方程:| | ( | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | ÷ | k | × | 2 | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ) | + | 28 | ÷ | ( | 3 | − | k | × | 2 | ) | = | 1440 |
| | ( | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | ÷ | k | × | 2 | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 1440 | ( | 3 | − | k | × | 2 | ) |
去掉方程左边的一个括号:
| | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | ÷ | k | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 1440 | ( | 3 | − | k | × | 2 | ) |
去掉方程右边的一个括号:
| | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | ÷ | k | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 1440 | × | 3 | − | 1440 | k | × | 2 |
方程化简为:
| | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | ÷ | k | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 4320 | − | 2880 | k |
| | ( | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ) | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | k | + | 28 | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | k | + | 28 | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 2 | k | ( | 2 | k | + | 2 | ) | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 2 | ( | 2 | k | + | 2 | ) | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 4 | k | ( | 2 | k | + | 2 | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | ( | 2 | k | + | 2 | ) | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ( | 4 | k | ÷ | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 4 | k | × | 2 | k | ( | 3 | − | k | × | 2 | ) | + | 4 | k | × | 2 | ( | 3 | − | k | × | 2 | ) | + | 4 | ( | 2 | k | + | 2 | ) | ( | 3 | − | k | × | 2 | ) | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 8 | k | k | ( | 3 | − | k | × | 2 | ) | + | 8 | k | ( | 3 | − | k | × | 2 | ) | + | 4 | ( | 2 | k | + | 2 | ) | ( | 3 | − | k | × | 2 | ) | + | 1 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 8 | k | k | × | 3 | − | 8 | k | k | k | × | 2 | + | 8 | k | ( | 3 | − | k | × | 2 | ) | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 8 | k | ( | 3 | − | k | × | 2 | ) | + | 4 | ( | 2 | k | + | 2 | ) | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 24 | k | k | − | 16 | k | k | k | + | 8 | k | × | 3 | − | 8 | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 24 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 52 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 24 | k | k | − | 16 | k | k | k | + | 52 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 52 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 24 | k | k | − | 16 | k | k | k | + | 52 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 52 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 76 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 24 | k | k | − | 16 | k | k | k | + | 76 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 76 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程化简为:
| | 24 | k | k | − | 16 | k | k | k | + | 60 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
去掉方程左边的一个括号:
| | 24 | k | k | − | 16 | k | k | k | + | 60 | k | − | 16 | k | k | = | 4320 | k | − | 2880 | k | k |
方程的解为:
k1≈-8.123780 ,保留6位小数
k2≈6.967505 ,保留6位小数
有 2个解。
解程的详细方法请参阅:《方程的解法》
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