If $$x - \frac{1}{x} = 4{\text{,}}$$   then $$\left( {x + \frac{1}{x}} \right)$$   is equal to?

$$\eqalign{ & x - \frac{1}{x} = 4 \cr & \left( {{\text{on squaring }}} \right) \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} - 2 = 16 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} = 18 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 - 2 = 18 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 20 \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 20 \cr & \Rightarrow x + \frac{1}{x} = \sqrt {20} \cr & \Rightarrow x + \frac{1}{x} = \sqrt {4 \times 5} \cr & \Rightarrow x + \frac{1}{x} = 2\sqrt 5 \cr} $$