Do you hate square roots?

Algebra Level 4

\[\large{\begin{cases} x \sqrt{y} = 30 - y \sqrt{x} \\ x \sqrt{x} = 35 - y \sqrt{y} \end{cases}} \] Let \(x\) and \(y\) be positive real numbers satisfying the system of equations above. Find \(\sqrt{x^2+y^2+3}\).

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