If $x + \dfrac{1}{x} = 5$, then $x - \dfrac{1}{x}$ =

1. $\pm \sqrt{21}$

2. $\pm \sqrt{29}$

3. $\pm 3$

4. $\pm 2$

Given,

$x + \dfrac{1}{x} = 5$

Using identity,

$\Rightarrow \Big(x + \dfrac{1}{x}\Big)^2 = x^2 + \dfrac{1}{x^2} + 2 \times x \times \dfrac{1}{x}\\[1em] \Rightarrow (5)^2 = x^2 + \dfrac{1}{x^2} + 2 \\[1em] \Rightarrow 25 - 2 = x^2 + \dfrac{1}{x^2} \\[1em] \Rightarrow x^2 + \dfrac{1}{x^2} = 23\\[1em]$

We know that,

$\Rightarrow \Big(x - \dfrac{1}{x}\Big)^2 = x^2 + \dfrac{1}{x^2} - 2 \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big)^2 = 23 - 2 \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big)^2 = 21 \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big) = \pm \sqrt{21} \\[1em]$

Hence, Option 1 is the correct option.