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sqrt2 a^3+ 3/(ab-b^2) >= 10 when a>b>0

Source: Singapore Junior Math Olympiad 2019 2nd Round p4 SMO

March 26, 2020
inequalitiesalgebra

Problem Statement

Let a>b>0a>b>0. Prove that 2a3+3ab−b2≥10\sqrt2 a^3+ \frac{3}{ab-b^2}\ge 10 When does equality hold?
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