Can you find this!

$\large \displaystyle \text{Let } x - \frac{1}{x} = a\\ \large \displaystyle \text{Squaring on both sides}\\ \large \displaystyle \left(x - \frac{1}{x} \right)^2 = a^2\\ \large \displaystyle \implies x^2 + \frac{1}{x^2} - 2 \times x \times \frac{1}{x} = a^2\\ \large \displaystyle \implies x^2 + \frac{1}{x^2} - 2 = a^2\\ \large \displaystyle \left[\because x^2 + \frac{1}{x^2} = 171 \right]\\ \large \displaystyle \implies 171 - 2 = a^2\\ \large \displaystyle \implies a^2 = 169\\ \large \displaystyle \implies a = \sqrt{169} = \color{#3D99F6}{\boxed{13}}.$

$\large \displaystyle \therefore \text{The value of } x - \frac{1}{x} = \color{#D61F06}{\boxed{13}}.$