Show that if a and b have the same sign then:

|a + b| = |a| + |b|, and if a and b have opposite signs then:

|a + b| < |a| + |b|.

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- Aug 20th 2008, 10:56 PMflower3please؟?Show that if a and b have the same sign then:

|a + b| = |a| + |b|, and if a and b have opposite signs then:

|a + b| < |a| + |b|. - Aug 20th 2008, 11:44 PMwisterville
Hello,

If you are talking about real numbers,

all you have to do is divide into cases...

For example,

(i) a>0, b<0, b<-a: |a|=a, |b|=-b, |a+b|=-(a+b)=-a-b<a-b=|a|+|b|.

(ii) a>0, b<0, b>=-a: |a|=a, |b|=-b, |a+b|=a+b<a-b=|a|+|b|.

(iii) a>0, b>0: ...

etc.

bye.