IMO 1971 LL AUT3

Let a, b, c be positive real numbers, 0 < a \leqb \leqc. Prove that

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IMO 1971 LL AUT3

Origin: AUT

Problem

Let a, b, c be positive real numbers, 0 < a \leqb \leqc. Prove that for any positive real numbers x, y, z the following inequality holds: (ax + by + cz) x a + y b + z c \leq(x + y + z)2 (a + c)2 4ac .