Algebra · Algebraic identities · Symmetric expressions · Cubes · Systems of equations
The real numbers \(a\) and \(b\) satisfy
\[ a^3 = 3ab^2 + 11 , \qquad b^3 = 3a^2 b + 2 . \]
Compute the value of \(a^2 + b^2\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2005, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source