Valentine won't show it merci

Algebra Level 5

\[x+y+z+\frac{20}{\sqrt{x+z}}+\frac{20}{\sqrt{y+2}}\] Given that \(x,y\) and \(z\) are positive reals satisfying \(x^2+y^2+z^2+2xy-3x-3y-3z=0\), find the minimum of the expression above.

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