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2x−2y+1z=120142y−2z+1x=120142z−2x+1y=12014 \begin{aligned} 2x-2y + \frac 1 z &=& \frac 1 {2014} \\ 2y - 2z + \frac 1 x &=& \frac 1 {2014} \\ 2z - 2x + \frac 1 y &=& \frac 1 {2014} \\ \end{aligned} 2x−2y+z12y−2z+x12z−2x+y1===201412014120141
Find all positive real numbers x,y,zx,y,zx,y,z such that they satisfy the system of equation above. Submit your answer as x+yz−zxx + yz - zx x+yz−zx.
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