3. The equation about $x$
$$
x^{2}+a|x|+a^{2}-3=0\left(a \in \mathbf{R}_{+}\right)
$$

has a unique real solution. Then $a=$ $\qquad$
3. $\sqrt{3}$.

For the equation $x^{2}+a|x|+a^{2}-3=0$, if $x$ is a solution, then $-x$ is also a solution. According to the problem, it has a unique solution, so $x=-x$, which means the only real solution must be 0. Therefore, $a^{2}-3=0$ and $a>0$, hence $a=\sqrt{3}$.