Algebra · Inequalities · Sum of squares · Symmetric expressions · Equality cases · Real versus positive variables
Problem 4, 2005
Prove that for all real numbers \(a\) and \(b\),
\[ a(1 + b^2) + b(1 + a^2) \leq (1 + a^2)(1 + b^2) . \]
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Serbian Republic Competition (Republicko takmicenje) 2005, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source