Samir's system of equations

Algebra Level 4

Let xx and yy be positive numbers such that {x2+yxy=2013,y2+xxy=671. \begin{cases} x^2+y\sqrt{xy}=2013, \\ y^2+x\sqrt{xy}=671. \\ \end{cases}

If y2=aby^2 = \frac{a}{b} where aa and bb are positive coprime numbers, what is a+ba+b ?

This problem is posed by Samir K.

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