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TOT 1998 Autumn OS4 max product x_i when prod x_i=prod (1-x_i), x_i in (0,1)

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May 11, 2020
inequalitiesalgebramax

Problem Statement

Among all sets of real numbers {x1,x2,...,x20}\{ x_1 , x_2 , ... , x_{20} \} from the open interval (0,1)(0, 1 ) such that x1x2...x20=(1−x1)(1−x2)...(1−x20)x_1x_2...x_{20}= ( 1 - x_1 ) ( 1 -x_2 ) ... (1 - x_{20} ) find the one for which x1x2...x20x_1 x_2... x_{20} is maximal.
(A Cherniatiev)
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