Let be the solution of ^ -1 ( 2x+1 x+1 ) + ^ -1 ( 2x-1 x-1 ) = 2 ^ -1 (x+1) where

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let x1,x2,x3x_1, x_2, x_3 be the solution of tan⁡−1(2x+1x+1)+tan⁡−1(2x−1x−1)=2tan⁡−1(x+1)\tan^{-1}\left(\frac{2x+1}{x+1}\right) + \tan^{-1}\left(\frac{2x-1}{x-1}\right) = 2\tan^{-1}(x+1) where x1<x2<x3x_1 < x_2 < x_3, then 2x1+x2+x322x_1 + x_2 + x_3^2 is equal to

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