Algebra · Polynomial factorisation · Systems of equations · Quadratic forms
The real numbers \(x\) and \(y\) satisfy
\[ x^{3} + x^{2} + xy + x + y + 2 = 0 \qquad\text{and}\qquad y^{3} - y^{2} + 3y - x = 0 . \]
Determine the value of \(x - y\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2015, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source