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)
$$\eqalign{ & \frac{1}{{{x^2} + {a^2}}} = {x^2} - {a^2} \cr & 1 = {x^4} - {a^4} \cr & {x^4} = 1 + {a^4} \cr & x = {\left( {1 + {a^4}} \right)^{\frac{1}{4}}} \cr} $$This Question Belongs to Arithmetic Ability >> Algebra
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