总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 400(10-6)+(400+100(10-x))(x-6)+(4-6)(1200-400-400-100(10-x)) = 2500 的解.
题型:方程
解:原方程:| | 400 | ( | 10 | − | 6 | ) | + | ( | 400 | + | 100 | ( | 10 | − | x | ) | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) | = | 2500 |
去掉方程左边的括号:
| 方程左边 = | 400 | × | 10 | − | 400 | × | 6 | + | ( | 400 | + | 100 | ( | 10 | − | x | ) | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | 4000 | − | 2400 | + | ( | 400 | + | 100 | ( | 10 | − | x | ) | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | 1600 | + | ( | 400 | + | 100 | ( | 10 | − | x | ) | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | 1600 | + | 400 | ( | x | − | 6 | ) | + | 100 | ( | 10 | − | x | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | 1600 | + | 400 | x | − | 400 | × | 6 | + | 100 | ( | 10 | − | x | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | 1600 | + | 400 | x | − | 2400 | + | 100 | ( | 10 | − | x | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 800 | + | 400 | x | + | 100 | ( | 10 | − | x | ) | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 800 | + | 400 | x | + | 100 | × | 10 | ( | x | − | 6 | ) | − | 100 | x | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 800 | + | 400 | x | + | 1000 | ( | x | − | 6 | ) | − | 100 | x | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 800 | + | 400 | x | + | 1000 | x | − | 1000 | × | 6 | − | 100 | x | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 800 | + | 400 | x | + | 1000 | x | − | 6000 | − | 100 | x | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 1400 | x | − | 100 | x | ( | x | − | 6 | ) | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 1400 | x | − | 100 | x | x | + | 100 | x | × | 6 | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 1400 | x | − | 100 | x | x | + | 600 | x | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 2000 | x | − | 100 | x | x | + | ( | 4 | − | 6 | ) | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 2000 | x | − | 100 | x | x | + | 4 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) | − | 6 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 6800 | + | 2000 | x | − | 100 | x | x | + | 4 | × | 1200 | − | 4 | × | 400 | − | 4 | × | 400 |
| = | - | 6800 | + | 2000 | x | − | 100 | x | x | + | 4800 | − | 1600 | − | 1600 | − | 400 | ( | 10 | − | x | ) | − | 6 |
| = | - | 5200 | + | 2000 | x | − | 100 | x | x | − | 400 | ( | 10 | − | x | ) | − | 6 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 5200 | + | 2000 | x | − | 100 | x | x | − | 400 | × | 10 | + | 400 | x | − | 6 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 5200 | + | 2000 | x | − | 100 | x | x | − | 4000 | + | 400 | x | − | 6 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 9200 | + | 2400 | x | − | 100 | x | x | − | 6 | ( | 1200 | − | 400 | − | 400 | − | 100 | ( | 10 | − | x | ) | ) |
| = | - | 9200 | + | 2400 | x | − | 100 | x | x | − | 6 | × | 1200 | + | 6 | × | 400 | + | 6 | × | 400 |
| = | - | 9200 | + | 2400 | x | − | 100 | x | x | − | 7200 | + | 2400 | + | 2400 | + | 600 | ( | 10 | − | x | ) |
| = | - | 11600 | + | 2400 | x | − | 100 | x | x | + | 600 | ( | 10 | − | x | ) |
方程化为一般式后,用因式分解法化为:
( x - 9 )( x - 9 )=0
由
x - 9 = 0
x - 9 = 0
得:
x1=9
x2=9
有 2个解。
解一元二次方程的详细方法请参阅:《一元二次方程的解法》
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