6. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Consider the sets
$$
\begin{array}{l}
A=\left\{x \mid x^{2}-[x]=2\right\}, \\
B=\{x \mid-2<x<2\} .
\end{array}
$$

Then $A \cap B=$ . $\qquad$
2,6. $\{-1, \sqrt{3}\}$.
If $x \in B$, then $[x] \in\{-2,-1,0,1,2\}$.
Substituting the set $A$ we get
$$
\begin{array}{l}
x^{2} \in\{0,1,2,3,4\} \\
\Rightarrow x \in\{0, \pm 1, \pm \sqrt{2}, \pm \sqrt{3}, \pm 2\} .
\end{array}
$$

Upon verification, only $A \cap B=\{-1, \sqrt{3}\}$.