\[x^{2} + \frac{9}{x^{2}} = 55;\ \ \ x - \frac{3}{x} = ?\]
\[x^{2} - 2x \cdot \frac{3}{x} + \left( \frac{3}{x} \right)^{2} = 55 - 2x \cdot \frac{3}{x}\]
\[\left( x - \frac{3}{x} \right)^{2} = 55 - 6\]
\[\left( x - \frac{3}{x} \right)^{2} = 49\]
\[x - \frac{3}{x} = 7;\]
\[x - \frac{3}{x} = - 7.\]
\[Ответ:\ - 7;7.\]