MathDB

3

Part of 2019 Dutch BxMO TST

Problems(1)

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

Source: Dutch BxMO TST 2019 p3

1/10/2020
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.
algebrainequalities