Problem Solving

If 2^x + 2^y = x^2 + y^2, where x and y are nonnegative integers, what is the greatest possible value of |x -y|?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

OA is D

Well I don't really know the fundamental way of solving questions of these kind but I considering the time pressure, I will use the following method

the question ask for the difference between x and y

|x-y| = difference between x and y

so simply keep y= 0

so, 2^x + 2^0 = x^2 + 0

2^x +1 = x^2

this is possible only when x= 3

Hope this helps