If $x^2 + \dfrac{1}{x^2} = 27$, find the value of $x - \dfrac{1}{x}$.

By formula,

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

Substituting values in above equation, we get :

$\Rightarrow \Big(x - \dfrac{1}{x}\Big)^2 = 27 - 2 \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big)^2 = 25 \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big) = \sqrt{25} \\[1em] \Rightarrow \Big(x - \dfrac{1}{x}\Big) = \pm 5.$

Hence, $\Big(x - \dfrac{1}{x}\Big) = \pm 5.$