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y - \sqrt{y} < x - 1/4 < y + \sqrt{y} if x - \sqrt{x} < y - 1/4 <= x + \sqrt{x}

Source: 1991 Swedish Mathematical Competition p2

April 2, 2021

inequalitiesalgebra

Problem Statement

x, y

are positive reals such that

x - \sqrt{x} \le y - 1/4 \le x + \sqrt{x}

. Show that

y - \sqrt{y} \le x - 1/4 \le y + \sqrt{y}