总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (x-9)[(x-42)(x-56)-46*46]-225(x-56)-20*46*15-20[15*46+20(x-42)] = 0 的解.
题型:方程
解:原方程:| | ( | x | − | 9 | ) | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 20 | × | 46 | × | 15 | − | 20 | ( | 15 | × | 46 | + | 20 | ( | x | − | 42 | ) | ) | = | 0 |
| 方程左边 = | ( | x | − | 9 | ) | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 13800 | − | 20 | ( | 15 | × | 46 | + | 20 | ( | x | − | 42 | ) | ) |
方程化为:
| | ( | x | − | 9 | ) | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 13800 | − | 20 | ( | 15 | × | 46 | + | 20 | ( | x | − | 42 | ) | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | x | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 9 | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 13800 | − | 20 | ( | 15 | × | 46 | + | 20 | ( | x | − | 42 | ) | ) |
| = | x | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | x | × | 46 | × | 46 | − | 9 | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 13800 | − | 20 |
| = | x | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | x | × | 2116 | − | 9 | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) | − | 13800 | − | 20 | ( | 15 | × | 46 | + | 20 | ( | x | − | 42 | ) | ) |
| = | x | x | ( | x | − | 56 | ) | − | x | × | 42 | ( | x | − | 56 | ) | − | 2116 | x | − | 9 | ( | ( | x | − | 42 | ) | ( | x | − | 56 | ) | − | 46 | × | 46 | ) | − | 225 | ( | x | − | 56 | ) |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | ( | x | − | 56 | ) | − | 2116 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | x | × | 42 | × | 56 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | x | × | 2352 | − | 2116 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 236 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 740 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 740 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 740 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 1118 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 1118 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 1118 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 893 | x | − | 9 |
| = | x | x | x | − | x | x | × | 56 | − | x | × | 42 | x | + | 893 | x | − | 9 |
方程化为一般式后,有公因式:
( x - 4 )
由
x - 4 = 0
得:
不能由因式分解法得出的解:
x2≈0.792505 ,保留6位小数
x3≈102.207495 ,保留6位小数
有 3个解。
解程的详细方法请参阅:《方程的解法》
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