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If frac 1 x^2 + a^2 = x^2 - a^2 &nbsp...

This question belongs to Arithmetic Ability Algebra
Algebra
?

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

Answer & Solution
Correct Answer: Option D
$$\eqalign{ & \frac{1}{{{x^2} + {a^2}}} = {x^2} - {a^2} \cr & 1 = {x^4} - {a^4} \cr & {x^4} = 1 + {a^4} \cr & x = {\left( {1 + {a^4}} \right)^{\frac{1}{4}}} \cr} $$
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