IMO 1987 LL GBR26

Prove that if x, y, z are real numbers such that x2+y2+z2 = 2,

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IMO 1987 LL GBR26

Origin: GBR

Problem

Prove that if x, y, z are real numbers such that x2+y2+z2 = 2, then x + y + z \leqxyz + 2.