\[\boxed{\text{165\ (165).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x^{2} + \frac{1}{x^{2}} = 6;\ \ \ \ x - \frac{1}{x} = ?\]
\[\left( x - \frac{1}{x} \right)^{2} = x^{2} - 2 + \frac{1}{x^{2}} =\]
\[= 6 - 2 = 4\]
\[\left( x - \frac{1}{x} \right)^{2} = 4\]
\[\left\{ \begin{matrix} x - \frac{1}{x} = 2\ \ \ \\ x - \frac{1}{x} = - 2 \\ \end{matrix} \right.\ \]
\[Ответ:2;\ \ - 2.\]