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Algebra Level 5

\[ \large{\begin{cases} x^2+y^2+xy=1 \\ x^2 + z^2 + xz = 3 \\ z^2 +y^2 + zy = 4 \end{cases} }\]

If \(x,y\) and \(z\) are positive real numbers satisfying the system of equations above, find \((x+y+z)^2 \).

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