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Math Help - Sum of 2 Squares

  1. #1
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    Sum of 2 Squares

    How do you express x^2 + xy + y^2 as the sum of two squares

    Any help much appreciated.

    ViperRobK
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  2. #2
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    Hello, ViperRobK!

    How do you express x^2 + xy + y^2 as the sum of two squares?
    There is a way . . . but it's not "pleasant".


    Subtract and add 3xy\!:\quad x^2 + xy \:{\color{red}-\;3xy} + y^2 \;{\color{red}+\; 3xy}

    . . . . . .and we have: . x^2 - 2xy + y^2 + 3xy

    . . . . . . . and finally: . (x-y)^2 + (\sqrt{3xy})^2


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