If $$\frac{1}{{{x^2} + {a^2}}} = {x^2} - {a^2},$$    then the value of x is:

A. $${\left( {1 - {a^4}} \right)^{\frac{1}{4}}}$$

B. $$a$$

C. $${\left( {{a^4} - 1} \right)^{\frac{1}{4}}}$$

D. $${\left( {{a^4} + 1} \right)^{\frac{1}{4}}}$$

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & \frac{1}{{{x^2} + {a^2}}} = {x^2} - {a^2} \cr & 1 = {x^4} - {a^4} \cr & {x^4} = 1 + {a^4} \cr & x = {\left( {1 + {a^4}} \right)^{\frac{1}{4}}} \cr} $$