MathDB

\sqrt{(1-a^2)(1-b^2)} > \frac{a}{2b}+\frac{b}{2a}-ab-\frac{1}{8ab}

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1994 p6

February 20, 2020

inequalitiesalgebra

Problem Statement

Show that from any four distinct numbers lying in the interval

(0,1)

one can choose two distinct numbers

a

and

b

such that

\sqrt{(1-a^2)(1-b^2)} > \frac{a}{2b}+\frac{b}{2a}-ab-\frac{1}{8ab}