MathDB

If t^4 + t^{-4} = 2023, then determine t^3 + t^{-3}

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

March 20, 2024

algebraPolynomials

Problem Statement

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.