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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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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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a = 2014

∴ x = y = z = 2014

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