If x = a + 1/a and y = a - 1/a then x^4 + y^4 - 2x^2y^2 is equal to:

Answer: Option D

$$\begin{array}{rl}& x=a+\frac{1}{a},y=a-\frac{1}{a}\\ & \text{Let}\Rightarrow a=1\\ & x=1+\frac{1}{1}=2\\ & y=1-1=0\\ & \sqrt{x^4+y^4-2x^2{y}^2}\\ & =\sqrt{16+0-0}\\ & =4\end{array}$$