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Let xxx and yyy 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} {x2+yxy=2013,y2+xxy=671.
If y2=aby^2 = \frac{a}{b} y2=ba where aaa and bbb are positive coprime numbers, what is a+ba+b a+b?
This problem is posed by Samir K.
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