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(a)x^3 - y^3 >= 4x => x^2 > 2y (b) x^5 - y^3 >= 2x => $x^3 >= 2y

Source: Dutch BxMO TST 2019 p3

January 10, 2020
algebrainequalities

Problem Statement

Let xx and yy be positive real numbers. 1. Prove: if x3−y3≥4xx^3 - y^3 \ge 4x, then x2>2yx^2 > 2y. 2. Prove: if x5−y3≥2xx^5 - y^3 \ge 2x, then x3≥2yx^3 \ge 2y.
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