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Math Help - Why is the following true ?!!

  1. #1
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    Why is the following true ?!!

    Sorry to have to ask this, but I am stuck...

    Why is this true:

     2\left| x_1 x_2 \right| \leq x_1^2 + x_2^2$

    ???

    How do I reach that conclusion from:

    (x_1 + x_2)^2 = x_1^2 + x_2^2 + 2x_1x_2

    ???

    Cheers in advance!
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  2. #2
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    Re: Why is the following true ?!!

    Quote Originally Posted by howdigethere View Post
    How do I reach that conclusion from:

    (x_1 + x_2)^2 = x_1^2 + x_2^2 + 2x_1x_2
    Not only (x_1 + x_2)^2\ge0, but also (x_1 - x_2)^2\ge0. And either -2x_1x_2=|x_1x_2| or 2x_1x_2=|x_1x_2|.
    Thanks from howdigethere
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  3. #3
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    Re: Why is the following true ?!!

    dang.

    Thank You emakarov!
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