Problem

Source: 2023 OLCOMA Costa Rica National Olympiad, Final Round, 3.5

Tags: algebra, Polynomials



Let $t$ be a positive real number such that $t^4 + t^{-4} = 2023$. Determine the value of $t^3 + t^{-3}$ in the form of $a\sqrt b$, where $a$ and $b$ are positive integers.