If 2x² + 5x + 1 = 0, then one of the value of $$x - \frac{1}{{2x}}$$  is:

Solution (By Examveda Team)

$$\eqalign{ & 2{x^2} + 5x + 1 = 0 \cr & 2{x^2} + 1 = - 5x \cr & 2x + \frac{1}{x} = - 5 \cr & {\text{divide '2' both sides}} \cr & x + \frac{1}{{2x}} = - \frac{5}{2} \cr & a - b = \sqrt {{{\left( {a + b} \right)}^2} - 4ab} \cr & x - \frac{1}{{2x}} = \sqrt {{{\left( { - \frac{5}{2}} \right)}^2} - 4 \times x \times \frac{1}{{2x}}} \cr & = \sqrt {\frac{{25}}{2} - 2} \cr & = \frac{{\sqrt {17} }}{2} \cr} $$