总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 3*(1+x)*15+3*(1+x)*14+3*(1+x)*13+3*(1+x)*12+3*(1+x)*11 = 22 的解.
题型:方程
解:原方程:| | 3 | ( | 1 | + | x | ) | × | 15 | + | 3 | ( | 1 | + | x | ) | × | 14 | + | 3 | ( | 1 | + | x | ) | × | 13 | + | 3 | ( | 1 | + | x | ) | × | 12 | = | 22 |
| 方程左边 = | 45 | ( | 1 | + | x | ) | + | 42 | ( | 1 | + | x | ) | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
方程化为:
| | 45 | ( | 1 | + | x | ) | + | 42 | ( | 1 | + | x | ) | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) | = | 22 |
去掉方程左边的括号:
| 方程左边 = | 45 | × | 1 | + | 45 | x | + | 42 | ( | 1 | + | x | ) | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 45 | + | 45 | x | + | 42 | ( | 1 | + | x | ) | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 45 | + | 45 | x | + | 42 | × | 1 | + | 42 | x | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 |
| = | 45 | + | 45 | x | + | 42 | + | 42 | x | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 87 | + | 87 | x | + | 39 | ( | 1 | + | x | ) | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 87 | + | 87 | x | + | 39 | × | 1 | + | 39 | x | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 87 | + | 87 | x | + | 39 | + | 39 | x | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 126 | + | 126 | x | + | 36 | ( | 1 | + | x | ) | + | 33 | ( | 1 | + | x | ) |
| = | 126 | + | 126 | x | + | 36 | × | 1 | + | 36 | x | + | 33 | ( | 1 | + | x | ) |
| = | 126 | + | 126 | x | + | 36 | + | 36 | x | + | 33 | ( | 1 | + | x | ) |
| = | 162 | + | 162 | x | + | 33 | ( | 1 | + | x | ) |
| = | 162 | + | 162 | x | + | 33 | × | 1 | + | 33 | x |
| = | 162 | + | 162 | x | + | 33 | + | 33 | x |
方程化为:
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。
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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