a=9 and b=4
After analyzing the two equations, we can conclude that A and B must be perfect square integers.
As both of their square roots end up forming integers after being added by eachother.
So I would guess and check from there.
They both should be less than 121 because the largest integer in the equations is 11.
So I would guess all perfect squares from 1 to 121.
Not the best strategy...