已知|a|=|c|,化简|a-b|-|a+b|+|a+c|+|c-b|
问题描述:
已知|a|=|c|,化简|a-b|-|a+b|+|a+c|+|c-b|
答
|a|=|c|,则a=c或者a=-c当a=c时|a-b|-|a+b|+|a+c|+|c-b| =|a-b|-|a+b|+|a+a|+|a-b| =2|a-b|-|a+b|+2|a|当a=-c时c=-a|a-b|-|a+b|+|a+c|+|c-b| =|a-b|-|a+b|+|a-a|+|-a-b|=|a-b|-|a+b|+0+|a-b|=|a-b|