X and Y are in Roots!

Algebra Level 4

\[\begin{eqnarray} 4x + y + 4\sqrt{xy} - 36\sqrt{x} - 18\sqrt{y} + 80 = 0 \end{eqnarray} \]

Let \(x\) and \(y\) be in the interval \( [0,1000] \). Find the number of integer pairs \( (x,y)\) satisfying the equation above.


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