The 3 variable square and product

Algebra Level 3

{x2yz=37y2xz=1z2xy=35 \large { \begin{cases} {x^2-yz=37 } \\ {y^2- xz = 1 } \\ {z^2-xy=-35 } \end{cases} }

If x,yx,y and zz are positive numbers that satisfy the system of equations above, find the value of 10000x+100y+z10000x + 100y + z.

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