3. Given $A=\left\{x \mid x^{2}-m x+m^{2}-19=0\right\}, B=\left\{x \mid \log _{2}\left(x^{2}-5 x+\right.\right.$ $8)=1\}, C=\left\{x \mid x^{2}+2 x-8=0\right\}$, and $A \cap B \neq \varnothing, A \cap C=\varnothing$, find the value of $m$.
3. From the given, $B=\{2,3\}, C=\{2,-4\}$, then $3 \in A$, so $3^{2}-3 m+m^{2}-19=$ 0 , solving for $m$ yields $m=5$ or -2. Therefore, upon verification, $m=-2$.