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if x^2 + y^2 - 1 < xy then x + y - |x - y| < 2

Source: Czech-Polish-Slovak Junior Match 2016, individual p2 CPSJ

January 20, 2020

inequalitiesalgebra

Problem Statement

Let

x

and

y

be real numbers such that

x^2 + y^2 - 1 < xy

. Prove that

x + y - |x - y| < 2

.
Slovakia