If x and y are perfect squares such that x + y = 65 and x > y, what is the least possible value of x − y?

Question

The answer is 33 but I don't the fast solution. 

Answer 1

Since they are both perfect squares,  you know they're both positive.  Then one of them has to be greater than 33 (roughly half of 65).  The closest perfect square greater than 33 is 36, so the bigger of the two can be 36, 49 or 64 - the next perfect squares until you get to 65.

If x=36, then y=65-36 = 39, not a perfect square.

 

If x=49, then y=65 - 49 = 16, a perfect square, x-y = 33

If x = 64, y=1, also a perfect square, x-y = 63.

 

The least possible value is x=49, y=16, x-y = 33