If x and y are integers such that $\displaystyle (x-y)^2 +2y^2 = 27$ find the possible values of x.
p.s that's the complete question.
Any help would be so much appreciated!
Thank you in advance!
Solve this equation for x:
$\displaystyle x = y-\sqrt{27-2y^2}~\vee~ x = y+\sqrt{27-2y^2}$
Since $\displaystyle 27-2y^2 \geq 0$ the values of y are in $\displaystyle |y| \in \{1,2,3\}$
Plug in these values and check if x is an integer. I've got 4 solutions:
$\displaystyle (4, -1),\ (-4, 1),\ (6, 3),\ (-6, -3)$