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(x +y^3) (x^3 +y) >= 4x^2y^2 for x,y>=0

Source: Austria Beginners' Competition 2009 p2

December 26, 2021
inequalitiesalgebra

Problem Statement

Let xx and yy be nonnegative real numbers. Prove that (x+y3)(x3+y)≥4x2y2(x +y^3) (x^3 +y) \ge 4x^2y^2. When does equality holds?
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