olymmath

NL-BXMO-TST 2019 Problem 3

    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 .

    Dataset text AI-MO AoPS. Quoted with source.

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