Algebra · Inequality · Sum of squares · Am gm · Equality case
Let \(a\) and \(b\) be arbitrary nonnegative real numbers. Prove that
\[ (ab+1)(a+b) \ge 4ab , \]
and determine all pairs \((a,b)\) for which equality holds.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2007, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source