Algebra · Algebraic identities · Homogeneous polynomials · Binomial expansion · Systems of equations
Let \(a\) and \(b\) be real numbers satisfying
\[ a^3 - 3ab^2 = 8, \qquad b^3 - 3a^2 b = \sqrt{61} . \]
Find \(a^2 + b^2\).
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Serbian Regional Competition (Okruzno takmicenje) 1998, high school grade I, problem 2. The 1998 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source