16 If the roots of x3+px2+qx+p=0 are α,β,γ then prove that except one situation tan-1α+tan-1β+tan-1γ=nπ and then find - Maths - Inverse Trigonometric Functions

Question

16
I f   t h e   r o o t s   o f   x 3 + p x 2 + q
x + p = 0   a r e   α , β , γ   t h e
n   p r o v e   t h a t   e x c e p t   o n e
  s i t u a t i o n   tan - 1 α + tan - 1 β +
tan - 1 γ = n π   a n d   t h e n   f i n
d   t h e   s i t u a t i o n   w h e n   i t
  d o e s   n o t   h a p p e n

Md.Ashraf Khan · Accepted Answer

16. I f t h e r o o t s o f x 3 + p x 2 + q x + p = 0 a r e α , β , γ t h e n p r o v e t h a t e x c e p t o n e s i t u a t i o n tan - 1 α + tan - 1 β + tan - 1 γ = n π a n d t h e n f i n d t h e s i t u a t i o n w h e n i t d o e s n o t h a p p e n .

16.
$I f t h e r o o t s o f x^{3} + p x^{2} + q x + p = 0 a r e α, β, γ t h e n p r o v e t h a t (e x c e p t o n e s i t u a t i o n) \tan^{- 1} α + \tan^{- 1} β + \tan^{- 1} γ = n π a n d t h e n f i n d t h e s i t u a t i o n w h e n i t d o e s n o t h a p p e n .$