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If x = a + frac 1 a &nbsp and y...

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Algebra
?

If x = $$a + \frac{1}{a}$$  and y = $$a - \frac{1}{a}$$  then $$\sqrt {{x^4} + {y^4} - 2{x^2}{y^2}} $$    is equal to:

Answer & Solution
Correct Answer: Option D
$$\eqalign{ & x = a + \frac{1}{a},\,y = a - \frac{1}{a} \cr & {\text{Let}} \Rightarrow a = 1 \cr & x = 1 + \frac{1}{1} = 2 \cr & y = 1 - 1 = 0 \cr & \sqrt {{x^4} + {y^4} - 2{x^2}{y^2}} \cr & = \sqrt {16 + 0 - 0} \cr & = 4 \cr} $$
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