总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (x+3)(x+2)(4-x)+3+x+16-4x = 0 的解.
题型:方程
解:原方程:| | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 3 | + | x | + | 16 | − | 4 | x | = | 0 |
| 方程左边 = | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
方程化为:
| | ( | x | + | 3 | ) | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x | = | 0 |
去掉方程左边的括号:
| 方程左边 = | x | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
| = | x | x | ( | 4 | − | x | ) | + | x | × | 2 | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) | + | 19 | − | 3 | x |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 2 | ( | 4 | − | x | ) | + | 3 | ( | x | + | 2 | ) | ( | 4 | − | x | ) |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 2 | × | 4 | − | x | × | 2 | x |
| = | x | x | × | 4 | − | x | x | x | + | x | × | 8 | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 5 | x | − | x | × | 2 | x | + | 12 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 17 | x | − | x | × | 2 | x | − | 3 |
| = | x | x | × | 4 | − | x | x | x | + | 11 | x | − | x | × | 2 | x | − | 3 |
方程化为:
| | x | x | × | 4 | − | x | x | x | + | 11 | x | − | x | × | 2 | x | − | 3 | = | 0 |
x≈4.149063 ,保留6位小数
有 1个解。
解一元一次方程的详细方法请参阅:《一元一次方程的解法》
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