MathDB

sum 1/x(1-y ) >= 3 / ( xyz+(1-x)(1-y)(1-z) ) , for 0<x,y,z<1

Source: VI Soros Olympiad 1990-00 R1 9.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 27, 2024

algebrainequalities

Problem Statement

Let

x, y, z

be real numbers from interval

(0, 1)

. Prove that

\frac{1}{x(1-y)}+\frac{1}{y(1-x)}+\frac{1}{z(1-x)}\ge \frac{3}{xyz+(1-x)(1-y)(1-z)}