3. Given the equation about $x$: $x^{2}+a|x|+a^{2}-3=0(a \in \mathbf{R})$ has a unique real solution, then $a=$
3. $\sqrt{3}$ Detailed Explanation: Since $f(x)=x^{2}+a|x|+a^{2}-3$ is an even function, the only real solution must be 0, so $a^{2}-3=0$ and $a>0$. Therefore, $a=\sqrt{3}$.