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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)`A. 2B. 3C. 4D. none of these |
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Answer» Correct Answer - B `tan^(-1).(1)/(1 + 2x) + tan^(-1).(1)/(1 + 4x) = tan^(-1).(2)/(x^(2))` or `tan^(-1) [((1)/(1 + 2x) + (1)/(1+ 4x))/(1 - (1)/(1 + 2x) (1)/(1 + 4x))] = tan^(-1).(2)/(x^(2))` or `(2 + 6x)/(6x + 8x^(2)) = (2)/(x^(2))` or `6x^(3) - 14x^(2) - 12x = 0` or `x(x -3) (3x + 2) = 0` or `x = 3 " or " x = -2//3`(as `x != 0`) But for `x = -2//3`, L.H.S. `lt 0 and R.H.S. gt 0` Hence, the only solution is `x = 3` |
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