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Math Help - Sum of two squares proof. Help please.

  1. #1
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    Exclamation Sum of two squares proof. Help please.

    Good evening,

    I have this question for a mere tenth of my homework... and I'm a bit puzzled as to how to prove the theory... any help would be appreciated.

    "For any pair of numbers, x and y, 2(x^2+y^2) is the sum of the two squares." Prove this statement.

    I believe that the statement is true, and it is a proof by direct argument... however, my initial attempts at solving it algebraically failed miserably!

    I understand that it must have something to do with one of Fermat's theories, something to do with "4k+1" and prime numbers... but as of yet I've never learned anything about it..

    Please help!!

    Thanks, Milly.
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  2. #2
    MHF Contributor

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    Did you consider \left( {x + y} \right)^2  + \left( {x - y} \right)^2 ?
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  3. #3
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    Thumbs up Thank you!!!

    No I didn't consider it!
    I'm going to blame it on being back to school for two days after 6 weeks off!!
    Haha, thanks very much!!

    Milly.
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