Generator for a field extension

#ring_theory

Let $F$ be a field and let $α$ be an element that generates a field extension of $F$ of degree five. Prove that $α^{2}$ generates the same extension.

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Let $F$ be a field and let $\alpha$ be an element that generates a field extension of $F$ of degree five. Prove that $\alpha^2$ generates the same extension.