总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 4x2-16x+16 = (4x2+16-16x2)/(4x2+1+4x)+4x2+(16x-8x2)/(2x+1) 的解.
题型:方程
解:原方程: | 4 | x | × | 2 | − | 16 | x | + | 16 | = | ( | 4 | x | × | 2 | + | 16 | − | 16 | x | × | 2 | ) | ÷ | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | 4 | x | × | 2 | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ÷ | ( | 2 | x | + | 1 | ) |
方程两边同时乘以: | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
| 4 | x | × | 2 | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | − | 16 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | 16 | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | = | ( | 4 | x | × | 2 | + | 16 | − | 16 | x | × | 2 | ) | + | 4 | x | × | 2 | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ÷ | ( | 2 | x | + | 1 | ) | × | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程左边的一个括号:
| 4 | x | × | 2 | × | 4 | x | × | 2 | + | 4 | x | × | 2 | × | 1 | + | 4 | x | = | ( | 4 | x | × | 2 | + | 16 | − | 16 | x | × | 2 | ) | + | 4 | x | × | 2 | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ÷ | ( | 2 | x | + | 1 | ) | × | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程右边的一个括号:
| 4 | x | × | 2 | × | 4 | x | × | 2 | + | 4 | x | × | 2 | × | 1 | + | 4 | x | = | 4 | x | × | 2 | + | 16 | − | 16 | x | × | 2 | + | 4 | x | × | 2 | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) |
方程化简为:
| 64 | x | x | + | 8 | x | + | 32 | x | x | − | 16 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | 16 | = | 8 | x | + | 16 | − | 32 | x | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ÷ | ( | 2 | x | + | 1 | ) | × | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
方程化简为:
| 64 | x | x | + | 8 | x | + | 32 | x | x | − | 16 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | 16 | = | - | 24 | x | + | 16 | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ÷ | ( | 2 | x | + | 1 | ) | × | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
| 64 | x | x | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 2 | x | + | 1 | ) | + | 32 | x | x | ( | 2 | x | + | 1 | ) | − | 16 | = | - | 24 | x | ( | 2 | x | + | 1 | ) | + | 16 | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程左边的一个括号:
| 64 | x | x | × | 2 | x | + | 64 | x | x | × | 1 | + | 8 | x | ( | 2 | x | + | 1 | ) | = | - | 24 | x | ( | 2 | x | + | 1 | ) | + | 16 | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程右边的一个括号:
| 64 | x | x | × | 2 | x | + | 64 | x | x | × | 1 | + | 8 | x | ( | 2 | x | + | 1 | ) | = | - | 24 | x | × | 2 | x | − | 24 | x | × | 1 | + | 16 | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 8 | x | ( | 2 | x | + | 1 | ) | + | 32 | x | = | - | 48 | x | x | − | 24 | x | + | 16 | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) |
去掉方程左边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 8 | x | × | 2 | x | + | 8 | = | - | 48 | x | x | − | 24 | x | + | 16 | ( | 2 | x | + | 1 | ) | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) |
去掉方程右边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 8 | x | × | 2 | x | + | 8 | = | - | 48 | x | x | − | 24 | x | + | 16 | × | 2 | x | + | 16 | × | 1 | + | 8 | x |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | − | 24 | x | + | 32 | x | + | 16 | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程左边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 8 | x | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) | ( | 2 | x | + | 1 | ) | + | ( | 16 | x | − | 8 | x | × | 2 | ) | ( | 4 | x | × | 2 | + | 1 | + | 4 | x | ) |
去掉方程右边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 8 | x | × | 4 | x | × | 2 | ( | 2 | x | + | 1 | ) |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 64 | x | x | ( | 2 | x | + | 1 | ) | + | 8 | x |
去掉方程左边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 64 | x | x | ( | 2 | x | + | 1 | ) | + | 8 | x |
去掉方程右边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 64 | x | x | × | 2 | x | + | 64 |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
去掉方程左边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
去掉方程右边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 8 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
方程化简为:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 16 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
去掉方程左边的一个括号:
| 128 | x | x | x | + | 64 | x | x | + | 16 | x | x | + | 8 | x | = | - | 48 | x | x | + | 16 | x | + | 16 | + | 128 | x | x | x | + | 64 | x |
方程化为一般式后,有公因式:
( x +0 )
由
x + 0 = 0
得:
不能由因式分解法得出的解:
x2≈1.041667 ,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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