Arithmetic Aptitude :: Simplification

4. If (a^2 + b^2 + 1/a^2 + 1/b^2) = 4, then the value of (a^2 + b^2) will be

Answer: Option B

Explanation :

Given (a^2 + b^2 + 1/a^2 + 1/b^2) = 4
Simplify the above eq.
=> a^2 + 1/a^2 +b^2 + 1/b^2 = 4
=> (a-1/a)^2 + 2 + (b - 1/b)^2 + 2 = 4
=> (a-1/a)^2 + (b - 1/b)^2 = 0
=> (a - 1/a) = 0; (b - 1/b) = 0
=> a = b = (+-)1
so (a^2+b^2) = 1+1 = 2

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