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Junior Regional Olympiad - FBH 2018 Grade 8 Problem 4

Source:

September 19, 2018

inequalitiespositive real

Problem Statement

Let

a

b

and

c

be positive real numbers such that

a \geq b \geq c

. Prove the inequality:

\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \leq \frac{b}{a}+\frac{c}{b}+\frac{a}{c}