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Let $p(x,y),q(x,y)\in \mathbb{Q}[x,y]$. Assume that $p(0,0)=q(0,0)$. Is it generally possible to find a polynomial $r(x,y)\in\mathbb{Q}[x,y]$ irreducible in $\mathbb{Q}[x,y]$ such that $\mathbb{R}[x,y]...