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Math Help - please؟?

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    172

    please؟?

    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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  2. #2
    Member
    Joined
    Aug 2008
    Posts
    80
    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.
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