The number of positive solution satisfying the equation `tan^(-1)((1)/(2x+1))+tan^(-1)((1)/(4x+1))=tan^(-1)(2/(x^2))` is

Options

A. 1
B. 2
C. 8
D. 9

Explanation

To solve the equation \( \tan^{-1}\left(\frac{1}{2x+1}\right) + \tan^{-1}\left(\frac{1}{4x+1}\right) = \tan^{-1}\left(\frac{2}{x^2}\right) \), we can use the formula for the sum of inverse tangents:

\[ \tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\frac{a + b}{1 - ab}\right) \]

provided that \( ab < 1 \).

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