How to solve this nice math Exponential algebra problem | Olympiad Question | x=?,y=?

[@Ismailorakzai-u1m]

Interesting question

[@ArwindSah]

Easy way to solve this equation X² + 25XY +Y = 44 X² + 2XY +Y² -Y² + y =44 (X+Y)² - (Y² -Y) =44. (X+Y)² - (Y² - 2.Y.(1/2) +(1/2)² +(1/2)² = 44 (X+Y)² -(Y-1/2)²=44 -1/4 (X+Y+Y -1/2)(X+Y -Y+1/2) = 175/4 (X +2Y -1/2)(X +1/2)=175)4 4(X+2Y -1)(X+1/2) =175 (2X +4Y -1)(2X+1) =175 From here you can proceed as you have done. Thanks