3. $k \in \mathbf{R}$, the range of real roots $x$ for the equation (in terms of $x$) $x^{4}-2 k x^{2}+k^{2}+2 k-3=0$ is $\qquad$.
3. $[-\sqrt{2}, \sqrt{2}]$.
$k^{2}+2(1-x^{2}) k+x^{4}-3=0$. Since $k \in \mathbf{R}$, then $\Delta \geqslant 0, 4(1-x^{2})^{2}-4(x^{4}-3) \geqslant 0$, which gives $-\sqrt{2} \leqslant x \leqslant \sqrt{2}$