Explanation

Put t = √(x/y) > 0. Then t = 24/5 + 1/t gives 5t² − 24t − 5 = 0, i.e. (5t+1)(t−5) = 0, so t = 5. Hence x/y = 25; with x + y = 26 this gives y = 1, x = 25. Therefore xy = 25: option C.