If 2x² + 5x + 1 = 0, then find the value of \(\frac{1}{3}\) (x - \(\frac{1}{2x}\)).

\(\frac{\sqrt {17}}{6}\)

2x² + 5x + 1 = 0

divide by 2x

x + \(\frac{5}{2}\) + \(\frac{1}{2x}\) = 0

x + \(\frac{1}{2x}\) = -\(\frac{5}{2}\)

x - \(\frac{1}{2x}\) = \(\sqrt {(-\frac{5}{2})^2 - \frac{4}{2}}\) = \(\sqrt {\frac{17}{4}}\)

Now, \(\frac{1}{3}\) (x - \(\frac{1}{2x}\)) = \(\frac{\sqrt {17}}{3 × 2}\) = \(\frac{\sqrt {17}}{6}\)