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Homework Help: Triangle innequality proof question

  1. Nov 23, 2008 #1
    for "a" and "b" are real numbers prove that:

    http://img352.imageshack.us/my.php?image=34860604zw7.gif

    i need to use the triangle innequality
    |a|-|b|=< |a+b| <= |a| + |b|

    how to apply it to my question?
    it a long way from
    triangle innequality formula to the expression that i was given in the question

    ??
     
  2. jcsd
  3. Nov 23, 2008 #2
    The triangle inequality reads

    |x+y|<=|x|+|y|
    or
    |x|>=|x+y|-|y|

    for any two vectors x,y

    Take in particular

    x=a-b, y=b

    and

    x=b-a, y=a

    What do you get?
    Then use, |a-b|=|b-a| and the fact that if |a-b| is greater than c and greater then -c, it must be greater than |c|. (What is c?)
     
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