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Ineq: a^2 < bc implies b^3 + ac^2 > ab(a+c)

Source: Czech-Polish-Slovak Match, 2011

August 9, 2011
inequalitiesinequalities unsolved

Problem Statement

Let aa, bb, cc be positive real numbers satisfying a2<bca^2<bc. Prove that b3+ac2>ab(a+c)b^3+ac^2>ab(a+c).
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