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CGMO 2019 Problem 6

    Let 0≤x1≤x2≤⋯≤xn≤10\leq x_1\leq x_2\leq \cdots \leq x_n\leq 1 (n≥2).(n\geq 2). Prove that x1x2⋯xnn+(1−x1)(1−x2)⋯(1−xn)n≤1−(x1−xn)2n.\sqrt[n]{x_1x_2 \cdots x_n}+ \sqrt[n]{(1-x_1)(1-x_2)\cdots (1-x_n)}\leq \sqrt[n]{1-(x_1- x_n)^2}.

    Dataset text AI-MO AoPS. Quoted with source.

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