Algebra · Inequalities · Perfect squares · Two variable expressions · Equality cases
Prove that the inequality
\[ x^2 + y^2 + 1 \ge 2\bigl(xy - x + y\bigr) \]
holds for every pair of real numbers \(x\) and \(y\). When does equality occur?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2009, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source