总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 200*120(1+1/3*x)+280*(1-3/7*x)*80*(1+2*x) = 46400*(1+24/29*x) 的解.
题型:方程
解:原方程: | 200 | × | 120 | ( | 1 | + | 1 | ÷ | 3 | × | x | ) | + | 280 | ( | 1 | − | 3 | ÷ | 7 | × | x | ) | × | 80 | ( | 1 | + | 2 | x | ) | = | 46400 | ( | 1 | + | 24 | ÷ | 29 | × | x | ) |
方程左边 = | 24000 | ( | 1 | + | 1 | ÷ | 3 | × | x | ) | + | 22400 | ( | 1 | − | 3 | ÷ | 7 | × | x | ) | ( | 1 | + | 2 | x | ) |
方程化为:
| 24000 | ( | 1 | + | 1 | ÷ | 3 | × | x | ) | + | 22400 | ( | 1 | − | 3 | ÷ | 7 | × | x | ) | ( | 1 | + | 2 | x | ) | = | 46400 | ( | 1 | + | 24 | ÷ | 29 | × | x | ) |
去掉方程左边的括号:
方程左边 = | 24000 | × | 1 | + | 24000 | × | 1 | ÷ | 3 | × | x | + | 22400 | ( | 1 | − | 3 | ÷ | 7 | × | x | ) | ( | 1 | + | 2 | x | ) |
= | 24000 | + | 8000 | x | + | 22400 | ( | 1 | − | 3 | ÷ | 7 | × | x | ) | ( | 1 | + | 2 | x | ) |
= | 24000 | + | 8000 | x | + | 22400 | × | 1 | ( | 1 | + | 2 | x | ) | − | 22400 | × | 3 | ÷ | 7 | × | x | ( | 1 | + | 2 | x | ) |
= | 24000 | + | 8000 | x | + | 22400 | ( | 1 | + | 2 | x | ) | − | 9600 | x | ( | 1 | + | 2 | x | ) |
= | 24000 | + | 8000 | x | + | 22400 | × | 1 | + | 22400 | × | 2 | x | − | 9600 | x | ( | 1 | + | 2 | x | ) |
= | 24000 | + | 8000 | x | + | 22400 | + | 44800 | x | − | 9600 | x | ( | 1 | + | 2 | x | ) |
= | 46400 | + | 52800 | x | − | 9600 | x | ( | 1 | + | 2 | x | ) |
= | 46400 | + | 52800 | x | − | 9600 | x | × | 1 | − | 9600 | x | × | 2 | x |
= | 46400 | + | 52800 | x | − | 9600 | x | − | 19200 | x | x |
= | 46400 | + | 43200 | x | − | 19200 | x | x |
方程化为:
| 46400 | + | 43200 | x | − | 19200 | x | x | = | 46400 | ( | 1 | + | 24 | ÷ | 29 | × | x | ) |
去掉方程右边的括号:
方程右边 = | 46400 | × | 1 | + | 46400 | × | 24 | ÷ | 29 | × | x |
方程化为:
| 46400 | + | 43200 | x | − | 19200 | x | x | = | 46400 | + | 38400 | x |
方程化为一般式后,用因式分解法化为:
( x +0 )( 4x - 1 )=0
由
x + 0 = 0
4x - 1 = 0
得:
x1=0
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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