olymmath

JBMO-SL 2012 A5

  • Answer

Find the largest positive integer nn for which the inequality

a+b+cabc+1+abcn≤52\frac{a+b+c}{a b c+1}+\sqrt[n]{a b c} \leq \frac{5}{2}

holds for all a,b,c∈[0,1]a, b, c \in[0,1]. Here abc1=abc\sqrt[1]{a b c}=a b c.

Dataset text NuminaMath olympiads. Quoted with source.

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