If the roots of the equation `x^(3) -10 x + 11 = 0` are u, v, and w, then the value of `3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1 w)` is ____

If the roots of the equation `x^(3) -10 x + 11 = 0` are u, v, and w, t

1.	If the roots of the equation `x^(3) -10 x + 11 = 0` are u, v, and w, then the value of `3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1 w)` is ____
Answer» Correct Answer - 6 Let `tan^(-1) u = alpha " or " tan alpha = u` `tan^(-1) v = beta " or " tan beta = v` `tan^(-1) w = gamma " or " tan gamma = w` `tan (alpha + beta + gamma) = (s_(1) -s_(3))/(1 - s_(2)) = (0 -(-11))/(1-(-10)) = (11)/(11) = 1` `:. alpha + beta + gamma = tan^(-1) (1) = (pi)/(4)` `rArr 3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1) w) = 6`

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