Needs a elegant solution apart from hit and trial (1)

Algebra Level 2

{x+y=27x−y=1 \begin{cases} x+\sqrt y = 27 \\ \sqrt x - y = 1 \end{cases}

Given that xx and yy are positive integers satisfying the system of equations above, find x+yx+y.

Abhisek Mohanty by Abhisek Mohanty
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