Prove by Induction that every term of the following sequence is irrational – math.stackexchange.com

Prove by Induction that every term of the following sequence is irrational – math.stackexchange.com

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Let $x_1 = (44)^{1/2}$ and $x_{n+1} = (3x_n + 1)^{1/2}$ for $n\geq 1$. Prove that $x_n$ is irrational for every $n\geq 1$. I really have no idea how to proceed, I couldn't even find a nice closed ...

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