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Math Help - triangle inequality

  1. #1
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    triangle inequality

    How do I prove the following identity?

    | |x| -|y| | <= |x - y|

    Thank you
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  2. #2
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    Quote Originally Posted by PersaGell View Post
    How do I prove the following identity?

    | |x| -|y| | <= |x - y|

    Thank you
    |xy|\geq xy

    -2|x||y|\leq -2xy

    x^2-2|x||y|+y^2 \leq x^2 - 2xy + y^2

    0 \leq (|x|-|y|)^2 \leq (x-y)^2

    \sqrt{(|x|-|y|)^2} \leq \sqrt{(x-y)^2}

    ||x|-|y||\leq |x-y|
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  3. #3
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    Here is a second way.
    Attached Thumbnails Attached Thumbnails triangle inequality-tri-ineq.gif  
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