总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 25950*(1+x/12*8)+25950*(1+x/12*9)+25950*(1+x/12*10)+25950*(1+x/12*11)+25950*(1+x/12*12) = 50000 的解.
题型:方程
解:原方程:| | 25950 | ( | 1 | + | x | ÷ | 12 | × | 8 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 9 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) | = | 50000 |
去掉方程左边的括号:
| 方程左边 = | 25950 | × | 1 | + | 25950 | x | ÷ | 12 | × | 8 | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 9 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) |
| = | 25950 | + | 17300 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 9 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 25950 | + | 17300 | x | + | 25950 | × | 1 | + | 25950 | x | ÷ | 12 | × | 9 | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 |
| = | 25950 | + | 17300 | x | + | 25950 | + | 38925 2 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 51900 | + | 73525 2 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 10 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 51900 | + | 73525 2 | x | + | 25950 | × | 1 | + | 25950 | x | ÷ | 12 | × | 10 | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 |
| = | 51900 | + | 73525 2 | x | + | 25950 | + | 21625 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 77850 | + | 116775 2 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 11 | ) | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 77850 | + | 116775 2 | x | + | 25950 | × | 1 | + | 25950 | x | ÷ | 12 | × | 11 | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 77850 | + | 116775 2 | x | + | 25950 | + | 47575 2 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 103800 | + | 82175 | x | + | 25950 | ( | 1 | + | x | ÷ | 12 | × | 12 | ) |
| = | 103800 | + | 82175 | x | + | 25950 | × | 1 | + | 25950 | x | ÷ | 12 | × | 12 |
| = | 103800 | + | 82175 | x | + | 25950 | + | 25950 | x |
方程化为:
| | 129750 | + | 108125 | x | = | 50000 |
移项:即,把含有未知数的项移到方程左边,把只含有常数的项移到方程的右边。
注意,移项时,该项前面的正负号要改变,即,正号变为负号,而负号要改变为正号。这与方程两边同时加上或者减去该项是等价的。
| | 108125 | x | = | 50000 | − | 129750 |
合并方程右边的各项:
把未知数的系数化为 1:
得:
把结果化为小数形式:
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