总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 100×200+(100-x)(200+2x)+50×[800-200-(200+2x)]-60×800 = 9200 的解.
题型:方程
解:原方程:| | 100 | × | 200 | + | ( | 100 | − | x | ) | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) | − | 60 | × | 800 | = | 9200 |
| 方程左边 = | 20000 | + | ( | 100 | − | x | ) | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) | − | 48000 |
| = | - | 28000 | + | ( | 100 | − | x | ) | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
方程化为:
| | - | 28000 | + | ( | 100 | − | x | ) | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) | = | 9200 |
去掉方程左边的括号:
| 方程左边 = | - | 28000 | + | 100 | ( | 200 | + | 2 | x | ) | − | x | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 28000 | + | 100 | × | 200 | + | 100 | × | 2 | x | − | x | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 28000 | + | 20000 | + | 200 | x | − | x | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 8000 | + | 200 | x | − | x | ( | 200 | + | 2 | x | ) | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 8000 | + | 200 | x | − | x | × | 200 | − | x | × | 2 | x | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 8000 | + | 0 | x | − | x | × | 2 | x | + | 50 | ( | 800 | − | 200 | − | ( | 200 | + | 2 | x | ) | ) |
| = | - | 8000 | − | x | × | 2 | x | + | 50 | × | 800 | − | 50 | × | 200 | − | 50 | ( | 200 | + | 2 | x | ) |
| = | - | 8000 | − | x | × | 2 | x | + | 40000 | − | 10000 | − | 50 | ( | 200 | + | 2 | x | ) |
| = | 22000 | − | x | × | 2 | x | − | 50 | ( | 200 | + | 2 | x | ) |
| = | 22000 | − | x | × | 2 | x | − | 50 | × | 200 | − | 50 | × | 2 | x |
| = | 22000 | − | x | × | 2 | x | − | 10000 | − | 100 | x |
| = | 12000 | − | x | × | 2 | x | − | 100 | x |
方程化为:
| | 12000 | − | x | × | 2 | x | − | 100 | x | = | 9200 |
方程化为一般式后,用因式分解法化为:
( x + 70 )( x - 20 )=0
由
x + 70 = 0
x - 20 = 0
得:
x1=-70
x2=20
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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