Algebra · Polynomial identities · Substitution · Quadratic relations · Degree reduction
A real number \(a\) satisfies \(a^{2} - \tfrac{1}{2}a = \tfrac{1}{4}\). What is the value of \(a^{3} - \tfrac{1}{2}a\)?
- A \(-\tfrac{1}{4}\)
- B \(\tfrac{1}{4}\)
- C \(\tfrac{1}{2}\)
- D \(4\)
- E \(\tfrac{1}{8}\)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2018, 1. letnik, category A, problem A2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source