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Algebra Level 4

The positive reals x,yx,y and zz satisfy the given equations:

x2+xy+y23=25x^{2}+xy+\frac{y^{2}}{3}=25

z2+y23=9z^{2}+\frac{y^{2}}{3}=9

z2+zx+x2=16z^{2}+zx+x^{2}=16

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

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