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RU-ALLRUSSIAN 1989 Problem 10

    A triangle with perimeter 1 has side lengths a, b, c. Show that a2+b2+c2+4abc<1/2\mathrm{a}^2 +\mathrm{b}^2 +\mathrm{c}^2 +4\mathrm{abc}< 1 / 2 .

    Dataset text NuminaMath olympiads. Quoted with source.

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