Find all positive real numbers x, y, z s...

Find all positive real numbers x, y, z such that:
`2x-2y + 1/z = 1/(2014), 2y-2z + 1/x = 1/(2014), 2z-2x + 1/y = 1/(2014)`

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The correct Answer is:

`x=y=z=2014`

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