olymmath

AT-OEMO-REG 2008 Problem 1

    Show: For all real numbers a,b,ca,b,c with 0<a,b,c<10<a,b,c<1 is: a2bc+ab2c+abc2+(1−a)2(1−b)(1−c)+(1−a)(1−b)2(1−c)+(1−a)(1−b)(1−c)2<3.\sqrt{a^2bc+ab^2c+abc^2}+\sqrt{(1-a)^2(1-b)(1-c)+(1-a)(1-b)^2(1-c)+(1-a)(1-b)(1-c)^2}<\sqrt{3}.

    Dataset text AI-MO AoPS. Quoted with source.

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