# Strange System of Equations

Algebra Level 5

$x$ and $y$ are real numbers satisfying the system of equations $\left\{\begin{array}{l}y^2+2y=x^2-2x+\sqrt{x}\\ x+y=\dfrac{1}{2\sqrt{x}}\end{array}\right.$

If the value of $xy$ can be expressed as $\dfrac{a+\sqrt{b}}{c}$ for integers $a,b,c$ with $b$ square-free, then what is $a+b+c$?

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