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Math Help - Triangle Inequality and Pseudometric

  1. #1
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    Triangle Inequality and Pseudometric

    The problem statement, all variables and given/known data

     d(x,y)=(a|x_1-y_1|^2+b|x_1-y_1||x_2-y_2|+c|x_2-y_2|^2)^{1/2<br /> <br />

    where a>0, b>0, c>0 and 4ac-b^2<0

    Show whether exhibits Triangle inequality?

    Relevant equations:

    (M4)   d(x,y) \leq d(x,z)+d(z,y)  (for all x,y and z in X)

    The attempt at a solution

    I started my solution by solving by squaring the both sides of the equation separately.

     d^2(x,y); [d(x,z)+d(z,y)]^2

    I am tending to think it does not satisfy the triangle inequality any other simple way to prove it? Also is this a pseudometric? if it does not satisfy the triangle inequality?
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  2. #2
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    Any help is greatly appreciated!
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