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(x^2 + 1)(y^2 + 1) >= 2(xy - 1)(x + y)

Source: Czech-Polish-Slovak Junior Match 2017, individual p3 CPSJ

February 20, 2020
inequalitiesalgebra

Problem Statement

Prove that for all real numbers x,yx, y holds (x2+1)(y2+1)≥2(xy−1)(x+y)(x^2 + 1)(y^2 + 1) \ge 2(xy - 1)(x + y). For which integers x,yx, y does equality occur?
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