IMO 1987 LL AUS4

Let a1, a2, a3, b1, b2, b3 be positive real numbers. Prove that

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IMO 1987 LL AUS4

Origin: AUS

Problem

Let a1, a2, a3, b1, b2, b3 be positive real numbers. Prove that (a1b2 + a2b1 + a1b3 + a3b1 + a2b3 + a3b2)2 \geq4(a1a2 + a2a3 + a3a1)(b1b2 + b2b3 + b3b1) and show that the two sides of the inequality are equal if and only if a1/b1 = a2/b2 = a3/b3.