\[8x + \frac{1}{x} = ?\]
\[64x^{2} + \frac{1}{x^{2}} = 65\]
\[64x^{2} + 16 + \frac{1}{x^{2}} = 65 + 16\]
\[\left( 8x + \frac{1}{x} \right)^{2} = 81\]
\[8x + \frac{1}{x} = \pm 9.\]