If $ X + \frac{1}{x} = - 14 $ and x < -1, what will be the value of $ x^2 -\frac{1}{x^2}$ ?

$ -112 \sqrt{3}$ $ 112 \sqrt{2}$ $ 140 \sqrt{2}$ $ -140 \sqrt{3}$

$ -112 \sqrt{3}$

If $ X + \frac{1}{x} = - 14 $ Then, x - \(\frac{1}{x}\) = \(\sqrt {-14^2 - 4}\) = \(\sqrt {192}\) = 8\(\sqrt {3}\)  The value of $ x^2 -\frac{1}{x^2}$ =  ($ X + \frac{1}{x}$) (x - \(\frac{1}{x}\)) $ x^2 -\frac{1}{x^2}$ =  (-14) ( 8\(\sqrt {3}\)) = -$ 112 \sqrt{3}$