MathDB

a/b+b/c+c/a>= 1/ab+1/bc+1/ca if a,b,c>0 and a+b+c>=1/a+1/b+1/c

Source: 2009 Romania JBMO TST 3.1

June 1, 2020

inequalitiesalgebra

Problem Statement

Let

a, b, c

be positive real number such that

a + b + c \ge \frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}

. Prove that

\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\ge \frac{1}{ab}+ \frac{1}{bc}+ \frac{1}{ca}