\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For \(A = X^3 - 1\) and \(B = X^2 - 1\) in \(\mathbb{R}[X]\), use the extended Euclidean algorithm to find \(U, V \in \mathbb{R}[X]\) such that \(A U + B V = A \wedge B\).
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