总述:本次共解1题。其中
☆方程1题
〖 1/1方程〗
作业:求方程 1700 = 1000*12%*(1+i)-1+1000*12%*(1+i)-2+1000*12%*(1+i)-4+1000*12%*(1+i)-5+1000*12%*(1+i)-6+1000*(1+i)-6 的解.
题型:方程
解:原方程: | 1700 | = | 1000 | × | 12 100 | ( | 1 | + | i | ) | − | 1 | + | 1000 | × | 12 100 | ( | 1 | + | i | ) | − | 2 | + | 1000 | × | 12 100 | ( | 1 | + | i | ) | − | 4 |
方程右边 = | 120 | ( | 1 | + | i | ) | − | 1 | + | 120 | ( | 1 | + | i | ) | − | 2 | + | 120 | ( | 1 | + | i | ) | − | 4 | + | 120 | ( | 1 | + | i | ) | − | 5 |
= | 120 | ( | 1 | + | i | ) | − | 24 | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 |
方程化为:
| 1700 | = | 120 | ( | 1 | + | i | ) | − | 24 | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 |
去掉方程右边的括号:
方程右边 = | 120 | × | 1 | + | 120 | i | − | 24 | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 |
= | 120 | + | 120 | i | − | 24 | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) |
= | 96 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 |
= | 96 | + | 120 | i | + | 120 | × | 1 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 |
= | 96 | + | 120 | i | + | 120 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) |
= | 216 | + | 240 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 216 | + | 240 | i | + | 120 | × | 1 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 |
= | 216 | + | 240 | i | + | 120 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 336 | + | 360 | i | + | 120 | ( | 1 | + | i | ) | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 336 | + | 360 | i | + | 120 | × | 1 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 336 | + | 360 | i | + | 120 | + | 120 | i | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 456 | + | 480 | i | + | 120 | ( | 1 | + | i | ) | + | 1000 | ( | 1 | + | i | ) |
= | 456 | + | 480 | i | + | 120 | × | 1 | + | 120 | i | + | 1000 | ( | 1 | + | i | ) |
= | 456 | + | 480 | i | + | 120 | + | 120 | i | + | 1000 | ( | 1 | + | i | ) |
= | 576 | + | 600 | i | + | 1000 | ( | 1 | + | i | ) |
= | 576 | + | 600 | i | + | 1000 | × | 1 | + | 1000 | i |
= | 576 | + | 600 | i | + | 1000 | + | 1000 | i |
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:
方程两边同时移项,改变符号 得:
方程的左边等于右边,则右边也 一定等于左边,即:
把未知数的系数化为 1:
得:
把结果化为小数形式:
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