\[\boxed{\mathbf{865\ (865).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[4x^{2} + \frac{1}{x^{2}} = 6\]
\[4x^{2} - 4x \cdot \frac{1}{x} + \frac{1}{x^{2}} + 4 = 6\]
\[\left( 2x - \frac{1}{x} \right)^{2} = 2\]
\[2x - \frac{1}{x} = \pm \sqrt{2}\]