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Simple cyclic inequality with simple constraint

Source: Southern Summer School, gr. 10

July 9, 2017
inequalitiescyclic inequalityFraction

Problem Statement

Let a,b,ca,b,c be the positive real numbers satisfying a2+b2+c2=3a^2+b^2+c^2=3. Prove that: ab(a+c)+bc(b+a)+ca(c+b)≥32.\frac{a}{b(a+c)}+\frac{b}{c(b+a)}+\frac{c}{a(c+b)}\geq \frac{3}{2}.
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