MathDB

1/(x-2)(y-2)(z-2)+8/(x+2)(y+2)(z+2)\le 1/ 32 if 2(xy + yz + zx) = xyz

Source: CRMO 2012 region 5 p8 Mumbai

September 30, 2018

inequalitiesInequality3-variable inequality

Problem Statement

Let

x, y, z

be positive real numbers such that

2(xy + yz + zx) = xyz

. Prove that

\frac{1}{(x-2)(y-2)(z-2)} + \frac{8}{(x+2)(y+2)(z+2)} \le \frac{1}{32}