\[x^{2} + \frac{9}{x^{2}} = 10\]
\[\left( x + \frac{3}{x} \right)^{2} - 6 = 10\]
\[\left( x + \frac{3}{x} \right)^{2} = 16\]
\[x + \frac{3}{x} = \pm 4.\ \]