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 | + | 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 | + | 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 | + | 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 | ) | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | ( | k | × | 2 | + | 1 | ) | = | 4320 | ( | k | × | 2 | + | 1 | ) | − | 2880 | k | ( | k | × | 2 | + | 1 | ) |
去掉方程左边的一个括号:
| | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | ( | k | × | 2 | + | 1 | ) | = | 4320 | ( | k | × | 2 | + | 1 | ) | − | 2880 | k | ( | k | × | 2 | + | 1 | ) |
去掉方程右边的一个括号:
| | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | ( | k | × | 2 | + | 1 | ) | = | 4320 | k | × | 2 | + | 4320 | × | 1 | − | 2880 | k | ( | k | × | 2 | + | 1 | ) |
方程化简为:
| | ( | 2 | k | + | 2 | ) | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | ( | k | × | 2 | + | 1 | ) | = | 8640 | k | + | 4320 | − | 2880 | k | ( | k | × | 2 | + | 1 | ) |
去掉方程左边的一个括号:
| | 2 | k | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 8640 | k | + | 4320 | − | 2880 | k | ( | k | × | 2 | + | 1 | ) |
去掉方程右边的一个括号:
| | 2 | k | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 8640 | k | + | 4320 | − | 2880 | k | k | × | 2 | − | 2880 | k | × | 1 |
方程化简为:
| | 2 | k | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 8640 | k | + | 4320 | − | 5760 | k | k | − | 2880 | k |
方程化简为:
| | 2 | k | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | ( | 2 | k | + | 2 | ) | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 28 | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 2 | k | × | 2 | k | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | k | × | 2 | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
方程化简为:
| | 4 | k | k | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 2 | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 4 | k | k | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | ( | ( | 1 | + | k | ) | ( | 1 | + | k | ) | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 4 | k | k | × | 1 | ( | 1 | + | k | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | 1 | + | k | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
方程化简为:
| | 4 | k | k | ( | 1 | + | k | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | 1 | + | k | ) | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 4 | k | k | × | 1 | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
方程化简为:
| | 4 | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 4 | k | k | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
去掉方程左边的一个括号:
| | 4 | k | k | × | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | × | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | = | 5760 | k | + | 4320 | − | 5760 | k | k |
方程化简为:
| | 16 | k | k | k | ÷ | ( | 3 | − | k | × | 2 | ) | × | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | = | 5760 | k | + | 4320 | − | 5760 | k | k |
| | 16 | k | k | k | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 3 | − | k | × | 2 | ) | + | 4 | k | k | k | ( | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ( | 4 | k | ÷ | ( | 3 | − | k | × | 2 | ) | ) | ) | ( | 3 | − | k | × | 2 | ) | = | 5760 | k | ( | 3 | − | k | × | 2 | ) | + | 4320 | ( | 3 | − | k | × | 2 | ) | − | 5760 | k | k | ( | 3 | − | k | × | 2 | ) |
方程的解为:
k≈1.174988 ,保留6位小数
有 1个解。
解方程的详细方法请参阅:《方程的解法》
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