IMO 1992 LL GBR21

Prove that if x, y, z > 1 and 1

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IMO 1992 LL GBR21

Origin: GBR

Problem

Prove that if x, y, z > 1 and 1 x + 1 y + 1 z = 2, then \sqrtx + y + z \geq \sqrt x −1 + y −1 + \sqrt z −1.