3888 = 36^2 * 3. Then x and y can be reduced to the form a*sqrt(3) and b*sqrt(3). The compound constraint a>b>=0 follows from x>y and the fact we are taking square roots.
Then a+b = 36. There are 19 ways to express 36 as an ordered sum of two nonnegative integers. One of these is 18+18, which fails the a>b requirement so the answer to the problem is 18 integer solutions.
Analytic Solution
