"Unpredictable Solution" Problem (Part 2)

Algebra Level 4

\[\begin{cases} xy-2x-y = 10 \\ yz-3y-2z = 14 \\ zx-z-3x=12 \end{cases} \]

Let \(x,y,z\) be all positive numbers satisfying the system of equations above. Find the value of \((x+y+z)^2 + x^2 + y^2 + z^2\).


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