Algebra · Symmetric expressions · Elementary symmetric polynomials · Sum of cubes · Exact radicals
Positive real numbers \(a\) and \(b\) have product \(1\), and the sum of their squares equals \(4\). Determine the exact value of
\[ a^{-3} + b^{-3} . \]
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2013, 1. letnik, category A, problem B1. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source