总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 (t-11)*(t-2)*(t-5)+320-64*(t-2)-100*(t-11)-4*(t-5) = 0 的解.
题型:方程
解:原方程:| | ( | t | − | 11 | ) | ( | t | − | 2 | ) | ( | t | − | 5 | ) | + | 320 | − | 64 | ( | t | − | 2 | ) | − | 100 | ( | t | − | 11 | ) | − | 4 | ( | t | − | 5 | ) | = | 0 |
去掉方程左边的括号:
| 方程左边 = | t | ( | t | − | 2 | ) | ( | t | − | 5 | ) | − | 11 | ( | t | − | 2 | ) | ( | t | − | 5 | ) | + | 320 | − | 64 | ( | t | − | 2 | ) | − | 100 | ( | t | − | 11 | ) | − | 4 |
| = | t | t | ( | t | − | 5 | ) | − | t | × | 2 | ( | t | − | 5 | ) | − | 11 | ( | t | − | 2 | ) | ( | t | − | 5 | ) | + | 320 | − | 64 | ( | t | − | 2 | ) |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | ( | t | − | 5 | ) | − | 11 | ( | t | − | 2 | ) | ( | t | − | 5 | ) |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | t | × | 2 | × | 5 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | t | × | 10 | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 10 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 10 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 10 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 10 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 65 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 65 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 65 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 87 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 87 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 87 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 23 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 23 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | + | 23 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | − | 77 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | − | 77 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | − | 77 | t | − | 11 |
| = | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | − | 81 | t | − | 11 |
方程化为:
| | t | t | t | − | t | t | × | 5 | − | t | × | 2 | t | − | 81 | t | − | 11 | = | 0 |
方程化为一般式后,用因式分解法化为:
( t + 9 )( t - 9 )( t - 18 )=0
由
t + 9 = 0
t - 9 = 0
t - 18 = 0
得:
t1=-9
t2=9
t3=18
有 3个解。
解程的详细方法请参阅:《方程的解法》
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