If $x^2 + \dfrac{1}{x^2} = 2$, the value of $x^2 - \dfrac{1}{x^2}$ is :

1. 0

2. 2

3. $\pm 2$

4. 8

By formula,

$\Rightarrow \Big(x^2 + \dfrac{1}{x^2}\Big)^2 - \Big(x^2 - \dfrac{1}{x^2}\Big)^2$ = 4.

Substituting values we get :

$\Rightarrow 2^2 - \Big(x^2 - \dfrac{1}{x^2}\Big)^2 = 4 \\[1em] \Rightarrow 4 - \Big(x^2 - \dfrac{1}{x^2}\Big)^2 = 4 \\[1em] \Rightarrow \Big(x^2 - \dfrac{1}{x^2}\Big)^2 = 4 - 4 \\[1em] \Rightarrow \Big(x^2 - \dfrac{1}{x^2}\Big)^2 = 0 \\[1em] \Rightarrow x^2 - \dfrac{1}{x^2} = 0.$

Hence, Option 1 is the correct option.