1. The solution set of the inequality $\left|x^{2}-2\right| \leqslant 2 x+1$ is
1. $[\sqrt{2}-1,3]$ Analysis: $\left|x^{2}-2\right| \leqslant 2 x+1 \Leftrightarrow\left\{\begin{array}{l}x^{2}-2 \leqslant 2 x+1 \\ x^{2}-2 \geqslant-2 x-1\end{array} \Leftrightarrow \sqrt{2}-1 \leqslant x \leqslant 3\right.$.