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Algebra Level 5

The positive reals \(x,y\) and \(z\) satisfy the given equations:

\[x^{2}+xy+\frac{y^{2}}{3}=25\]

\[z^{2}+\frac{y^{2}}{3}=9\]

\[z^{2}+zx+x^{2}=16\]

Find the value of \((xy+2yz+3xz)^{2}\).

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