If X + 1/x = - 14 and x < -1, what will be the value of x^2 -1/(x^2) ?

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}$