Samir's system of equations

Algebra Level 4

Let \(x\) and \(y\) be positive numbers such that \[ \begin{cases} x^2+y\sqrt{xy}=2013, \\ y^2+x\sqrt{xy}=671. \\ \end{cases} \]

If \(y^2 = \frac{a}{b} \) where \(a\) and \(b\) are positive coprime numbers, what is \(a+b \)?

This problem is posed by Samir K.

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