If $x + \dfrac{1}{x}$ = 2.5, the value of x is :

1. 4

2. 5 and $\dfrac{1}{5}$

3. 2 or $\dfrac{1}{2}$

4. 2 and $\dfrac{1}{2}$

Given,

$\Rightarrow x + \dfrac{1}{x} = 2.5 \\[1em] \Rightarrow \dfrac{x^2 + 1}{x} = \dfrac{25}{10} \\[1em] \Rightarrow 10(x^2 + 1) = 25x \\[1em] \Rightarrow 10x^2 + 10 = 25x \\[1em] \Rightarrow 10x^2 - 25x + 10 = 0 \\[1em] \Rightarrow 10x^2 - 20x - 5x + 10 = 0 \\[1em] \Rightarrow 10x(x - 2) - 5(x - 2) = 0 \\[1em] \Rightarrow (x - 2)(10x - 5) = 0 \\[1em] \Rightarrow x - 2 = 0 \text{ or } 10x - 5 =0 \\[1em] \Rightarrow x = 2 \text{ or } 10x = 5 \\[1em] \Rightarrow x = 2 \text{ or } x = \dfrac{5}{10} = \dfrac{1}{2}.$

Hence, Option 3 is the correct option.