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Source: IMO Shortlist 1993, Vietnam 2

March 25, 2006
inequalitiesfunctionfour variablesIMO Shortlist4-variable inequality

Problem Statement

Let a,b,c,da,b,c,d be four non-negative numbers satisfying a+b+c+d=1. a+b+c+d=1. Prove the inequality a⋅b⋅c+b⋅c⋅d+c⋅d⋅a+d⋅a⋅b≤127+17627⋅a⋅b⋅c⋅d. a \cdot b \cdot c + b \cdot c \cdot d + c \cdot d \cdot a + d \cdot a \cdot b \leq \frac{1}{27} + \frac{176}{27} \cdot a \cdot b \cdot c \cdot d.
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