Arithmetic mean of the non-zero solutions of the equation `tan^-1 (1/(2x + 1)) + tan^-1 (1/(4x + 1)) = tan^-1 (2/x^2)`

Options

A. 2
B. 3
C. 4
D. none of these

Explanation

To find the arithmetic mean of the non-zero solutions of 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 will follow these steps:

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