olymmath

JBMO-SL 2018 A3

    Let a,b,ca, b, c be positive real numbers. Prove that

    1ab(b+1)(c+1)+1bc(c+1)(a+1)+1ca(a+1)(b+1)≥3(1+abc)2\frac{1}{a b(b+1)(c+1)}+\frac{1}{b c(c+1)(a+1)}+\frac{1}{c a(a+1)(b+1)} \geq \frac{3}{(1+a b c)^{2}}

    Dataset text NuminaMath olympiads. Quoted with source.

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