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

Any help much appreciated.

ViperRobK

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- Sep 26th 2008, 09:03 AMViperRobKSum of 2 Squares
How do you express x^2 + xy + y^2 as the sum of two squares

Any help much appreciated.

ViperRobK - Sep 26th 2008, 11:03 AMSoroban
Hello, ViperRobK!

Quote:

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

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

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

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