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Comeback of inequalities (I'm sorry)

Source: Kyiv City MO 2024 Round 2, Problem 10.2

February 4, 2024
inequalitiesalgebra

Problem Statement

For any positive real numbers a,b,c,da, b, c, d, prove the following inequality: (a2+b2)(b2+c2)(c2+d2)(d2+a2)≥64abcd∣(a−b)(b−c)(c−d)(d−a)∣(a^2+b^2)(b^2+c^2)(c^2+d^2)(d^2+a^2) \geq 64abcd|(a-b)(b-c)(c-d)(d-a)| Proposed by Anton Trygub
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