总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (60-2X)x12x305x2+16x(120-2x12)x305 = Xx12x400x4+(120-2x12)*12x400x2 的解.
题型:方程
解:原方程: | ( | 60 | − | 2 | X | ) | X | × | 12 | X | × | 305 | X | × | 2 | + | 16 | X | ( | 120 | − | 2 | X | × | 12 | ) | X | × | 305 | = | X | X | × | 12 | X | × | 400 | X | × | 4 | + | ( | 120 | − | 2 | X | × | 12 | ) | × | 12 | X | × | 400 | X |
方程左边 = | ( | 60 | − | 2 | X | ) | X | × | 7320 | X | X | + | 4880 | X | ( | 120 | − | 2 | X | × | 12 | ) | X |
方程化为:
| ( | 60 | − | 2 | X | ) | X | × | 7320 | X | X | + | 4880 | X | ( | 120 | − | 2 | X | × | 12 | ) | X | = | X | X | × | 12 | X | × | 400 | X | × | 4 | + | ( | 120 | − | 2 | X | × | 12 | ) | × | 12 | X | × | 400 | X |
去掉方程左边的括号:
方程左边 = | 60 | X | × | 7320 | X | X | − | 2 | X | X | × | 7320 | X | X | + | 4880 |
= | 439200 | X | X | X | − | 14640 | X | X | X | X | + | 4880 | X | ( | 120 | − | 2 | X | × | 12 | ) |
= | 439200 | X | X | X | − | 14640 | X | X | X | X | + | 4880 | X | × | 120 |
= | 439200 | X | X | X | − | 14640 | X | X | X | X | + | 585600 | X | X |
方程化为:
| 439200 | X | X | X | − | 14640 | X | X | X | X | + | 585600 | X | X | = | X | X | × | 12 | X | × | 400 | X | × | 4 | + | ( | 120 | − | 2 | X | × | 12 | ) | × | 12 | X | × | 400 | X |
方程右边 = | X | X | × | 19200 | X | X | + | ( | 120 | − | 2 | X | × | 12 | ) | × | 9600 | X | X |
方程化为:
| 439200 | X | X | X | − | 14640 | X | X | X | X | + | 585600 | X | X | = | X | X | × | 19200 | X | X | + | ( | 120 | − | 2 | X | × | 12 | ) | × | 9600 | X | X |
去掉方程右边的括号:
方程右边 = | X | X | × | 19200 | X | X | + | 120 | × | 9600 | X | X | − | 2 | X | × | 12 |
= | X | X | × | 19200 | X | X | + | 1152000 | X | X | − | 230400 | X | X | X |
方程化为:
| 439200 | X | X | X | − | 14640 | X | X | X | X | + | 585600 | X | X | = | X | X | × | 19200 | X | X | + | 1152000 | X | X | − | 230400 | X | X | X |
方程化为一般式后,有公因式:
( X - 0 )( X - 0 )
由
X - 0 = 0
X - 0 = 0
得:
X1=0
X2=0
不能由因式分解法得出的解:
X3≈1.099202 ,保留6位小数
X4≈15.227039 ,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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