x is algebraic and let y = x + 3. Is y algebraic? and why is it?
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Originally Posted by thomasboateng x is algebraic and let y = x + 3. Is y algebraic? and why is it? Let f(x) be the irreducible polynomial for x over F. Then, the irreducible polynomial for y over F is f(y-3). So, y is algebraic.
More general, $\displaystyle \mathbb{A}=\{x\in\mathbb{R}:\; x\mbox{ & algebraic & over}\;\mathbb{Q}\}$ is a field (non finite extension of $\displaystyle \mathbb{Q}$)
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