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(1 +x/y)^3 +(1 +y/x)^3 >= 16 for x,y>0

Source: Norwegian Mathematical Olympiad 2012 - Abel Competition p4a

September 4, 2019
algebrainequalities

Problem Statement

Two positive numbers xx and yy are given. Show that (1+xy)3+(1+yx)3≥16\left(1 +\frac{x}{y} \right)^3 + \left(1 +\frac{y}{x}\right)^3 \ge 16.
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