Is x=y=z=0x=y=z=0?

Algebra Level 5

{(x−2)(y−2)=4(y−3)(z−3)=9(z−4)(x−4)=16 \large{\begin{cases} (x-2)(y-2)=4 \\ (y-3)(z-3)=9 \\ (z-4)(x-4)=16 \end{cases}}

Let x,yx,y and zz be positive rational numbers satisfying the system of equations above, find the value of 5x+7y−z5x+7y-z.

Piyush Kumar Behera by Piyush Kumar Behera
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