How do you express x^2 + xy + y^2 as the sum of two squares
Any help much appreciated.
ViperRobK
Hello, ViperRobK!
There is a way . . . but it's not "pleasant".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: .$\displaystyle (x-y)^2 + (\sqrt{3xy})^2$