Prove that for all real numbers $x, y$ holds $(x^2 + 1)(y^2 + 1) \ge 2(xy - 1)(x + y)$. For which integers $x, y$ does equality occur?
Problem
Source: Czech-Polish-Slovak Junior Match 2017, individual p3 CPSJ
Tags: inequalities, algebra
Source: Czech-Polish-Slovak Junior Match 2017, individual p3 CPSJ
Tags: inequalities, algebra
Prove that for all real numbers $x, y$ holds $(x^2 + 1)(y^2 + 1) \ge 2(xy - 1)(x + y)$. For which integers $x, y$ does equality occur?