2.
[tex]\it x+\sqrt2=3x(x+\sqrt2) \Rightarrow x+\sqrt2-3x(x+\sqrt2)=0 \Rightarrow (x+\sqrt2)(1-3x)=0\Rightarrow\\ \\ \\ \Rightarrow \begin{cases} \it x+\sqrt2=0 \Rightarrow x=-\sqrt2\ \not\in\mathbb{Q}\\ \\ \it 1-3x=0 \Rightarrow x=\dfrac{1}{3}\in\mathbb{Q}\end{cases}[/tex]
