Find all integers x,y.

Question

Find all integers x,y satisfying (x-y)^2+2y^2=27

Answer 1

Here's a hint to get you started - both terms on the left are non-negative, so neither one of them can be greater than 27.  

 

There aren't that many integer possibilities for y such that 2y^2 is no more than 27.  

 

Try them all, and determine which ones allow integer solution(s) for x.