Algebra · Inequality · Sum of squares · Am gm · Equality case
Problem 4, 2007
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.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
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