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

Answer: Option B

$$\begin{array}{rl}& x+\frac{1}{x}=-14\\ & x-\frac{1}{x}=\sqrt{{\left(-14\right)}^2-4}\\ & =\sqrt{196-4}\\ & =\sqrt{192}\\ & =8\sqrt{3}\\ & \therefore x<-1\\ & \left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)=-14x\left(8\sqrt{3}\right)\\ & x^2-\frac{1}{x^2}=+112\sqrt{3}\end{array}$$