Hướng dẫn giải

Chọn D

$A = \left\{{x \in \mathbb{R}\left|{x^2 + x + 1 = 0}\right.}\right\}$. Ta có $x^2 + x + 1 = 0\, \left({vn}\right)$ $\Rightarrow A = \emptyset$.

$B = \left\{{x \in \mathbb{N}\left|{x^2 - 2 = 0}\right.}\right\}$. Ta có $x^2 - 2 = 0$ $\Leftrightarrow x = \pm \sqrt 2 \notin \mathbb{N}$ $\Rightarrow B = \emptyset$

$C=\left\{ x\in \mathbb{Z}\left| \left( {{x}^{3}}-3 \right)\left( {{x}^{2}}+1 \right)=0 \right. \right\}$. Ta có $\left( {{x}^{3}}-3 \right)\left( {{x}^{2}}+1 \right)=0$ $\Leftrightarrow x = \sqrt[3]{3}\notin \mathbb{Z}$ $\Rightarrow C = \emptyset$

$D = \left\{{x \in \mathbb{Q}\left|{x\left({x^2 + 3}\right) = 0}\right.}\right\}$. Ta có $x\left({x^2 + 3}\right) = 0$ $\Leftrightarrow x = 0$ $\Rightarrow D = \left\{0 \right\}.$