Strange System of Equations

Algebra Level 5

xx and yy are real numbers satisfying the system of equations {y2+2y=x22x+xx+y=12x\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 xyxy can be expressed as a+bc\dfrac{a+\sqrt{b}}{c} for integers a,b,ca,b,c with bb square-free, then what is a+b+ca+b+c?

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