Question

已知|a|=1,|b|=3,则|a+b|-|a-b|的值是多少?

Answer 1

|a|=1,a=1或a=-1；

|b|=3,b=3或b=-3；

1,a=1,b=3,|a+b|-|a-b|=|1+3|-|1-3|=|4|-|-2|=4-2=2;

2,a=1,b=-3,|a+b|-|a-b|=|1-3|-|1+3|=|-2|-|4|=2-4=-2;

3,a=-1,b=3,|a+b|-|a-b|=|-1+3|-|-1-3|=|2|-|-4|=2-4=-2;

4,a=-1,b=-3,|a+b|-|a-b|=|-1-3|-|-1+3|=|-4|-|2|=4-2=2;

|a+b|-|a-b|= ±2