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Cyclic Inequality in 4 Variables with a+b+c+d=4

Source: MEMO Individual Competition, Question 1

September 24, 2007
inequalitiesinequalities proposed

Problem Statement

Let a,b,c,d a,b,c,d be positive real numbers with a\plus{}b\plus{}c\plus{}d \equal{} 4. Prove that a^{2}bc\plus{}b^{2}cd\plus{}c^{2}da\plus{}d^{2}ab\leq 4.
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