olymmath

JBMO-SL 2004 A1

    Prove that

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

    for any real numbers a,b,c≥1a, b, c \geq 1.

    Dataset text NuminaMath olympiads. Quoted with source.

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