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Inequality with sides of a triangle

Source: Bosnia and Herzegovina TST 2010 problem 5

March 30, 2014
inequalitiesinequalities proposed

Problem Statement

Let aa,bb and cc be sides of a triangle such that a+b+c≤2a+b+c\le2. Prove that −3<a3b+b3c+c3a−a3c−b3a−c3b<3-3<{\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}-\frac{a^3}{c}-\frac{b^3}{a}-\frac{c^3}{b}}<3
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