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Problem 1 — Symmetric Squares, Symmetric Products

Source: 46th Austrian Mathematical Olympiad National Competition Part 1 Problem 1

July 14, 2018
Austriaalgebrainequalities

Problem Statement

Let aa, bb, cc, dd be positive numbers. Prove that
(a2+b2+c2+d2)2≥(a+b)(b+c)(c+d)(d+a)(a^2 + b^2 + c^2 + d^2)^2 \ge (a+b)(b+c)(c+d)(d+a)
When does equality hold?
(Georg Anegg)
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