3. Know
$$
\begin{array}{l}
\left\{(x,-y) \mid(x+\sqrt{2})^{2}+y^{2}=a^{2}-3 a+2\right\} \cap \\
\left\{(x, y) \mid x^{2}+(y+\sqrt{2})^{2}<a\right\} \neq \varnothing .
\end{array}
$$

Then the range of real number $a$ is $\qquad$
$$
\begin{array}{l}
\sqrt{a^{2}-3 a+2}+\sqrt{a}>2>\sqrt{a^{2}-3 a+2}-\sqrt{a} \geqslant 0 \\
\text { or } \sqrt{a^{2}-3 a+2}+\sqrt{a}>2 \geqslant \sqrt{a}-\sqrt{a^{2}}-3 a+2>0 \text {. } \\
\text { Answer: (2.215 3,5.9717). } \\
\end{array}
$$