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ASU 169 All Soviet Union MO 1972 min of least of {x, (y+ 1/x), 1/y}, for x,y>0

Source:

July 3, 2019
inequalitiesalgebraminimummaximum

Problem Statement

Let x,yx,y be positive numbers, ss -- the least of {x,(y+1/x),1/y}\{ x, (y+ 1/x), 1/y\} What is the greatest possible value of ss? To what xx and yy does it correspond?
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