How I can prove that if there were $x$ and $y$ are algebraic numbers then $x+y$ and $x \cdot y$ are also algebraic numbers given that $x,y \in \mathbb R$?
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1https://math.stackexchange.com/questions/155122/how-to-prove-that-the-sum-and-product-of-two-algebraic-numbers-is-algebraic – Arctic Char Dec 12 '19 at 02:10