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a^2>3b if a^2b^2 + 18 abc > 4b^3+4a^3c+27c^2

Source: 2013 Swedish Mathematical Competition p6

April 30, 2021
inequalitiesalgebra

Problem Statement

Let a,b,ca, b, c, be real numbers such that a2b2+18abc>4b3+4a3c+27c2.a^2b^2 + 18 abc > 4b^3+4a^3c+27c^2 . Prove that a2>3ba^2>3b.
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