olymmath

JBMO-SL 2014 A3

    Let a,b,ca, b, c be positive real numbers such that abc=1a b c=1. Prove that:

    (a+1b)2+(b+1c)2+(c+1a)2≥3(a+b+c+1)\left(a+\frac{1}{b}\right)^{2}+\left(b+\frac{1}{c}\right)^{2}+\left(c+\frac{1}{a}\right)^{2} \geq 3(a+b+c+1)

    When does equality hold?

    Dataset text NuminaMath olympiads. Quoted with source.

    Also JBMO 2014 Problem 3.

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