Let $F$ a field and $\alpha$ and $\beta$ trascendental over $F$. Prove that $\alpha\beta$ or $\alpha+\beta$ are trascendental over $F$.
2026-03-26 21:53:59.1774562039
Are $\alpha\beta$ or $\alpha+\beta$ trascendental over $F$?
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Hint If $\alpha\beta$ and $\alpha +\beta$ are algebraic over $F$, then so are the solutions to $$x^2-(\alpha +\beta)x+\alpha\beta=0$$