olymmath

TW-TST 1992 Problem 3

    If x1,x2,...,xn(n>2)x_{1},x_{2},...,x_{n}(n>2) are positive real numbers with x1+x2+...+xn=1x_{1}+x_{2}+...+x_{n}=1 . Prove that x12x2+x22x3+...+xn2x1≤427x_{1}^{2}x_{2}+x_{2}^{2}x_{3}+...+x_{n}^{2}x_{1}\leq\frac{4}{27} .

    Dataset text AI-MO AoPS. Quoted with source.

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