Question

If `x_(1)`, `x_(2)` and `x_(3)` are the positive roots of the equation `x^(3)-6x^(2)+3px-2p=0`, `pinR`, then the value of `sin^(-1)((1)/(x_(1))+(1)/(x_(2)))+cos^(-1)((1)/(x_(2))+(1)/(x_(3)))-tan^(-1)((1)/(x_(3))+(1)/(x_(1)))` is equal to
A. `(pi)/(4)`
B. `(pi)/(2)`
C. `(3pi)/(4)`
D. `pi`

Answer 1

Correct Answer - A
`(a)` `x^(3)-6x^(2)+3px-2p=0`
`A.M.=(x_(1)+x_(2)+x_(3))/(3)=(6)/(3)=2`
`H.M.=(3)/((1)/(x_(1))+(1)/(x_(2))+(1)/(x_(3)))=(3x_(1)x_(2)x_(3))/(sumx_(1)x_(2))=2`
`:, A.M.=H.M.impliesx_(1)=x_(2)=x_(3)=2`
`sin^(-1)((1)/(x_(1))+(1)/(x_(2)))+cos^(-1)((1)/(x_(2))+(1)/(x_(3)))-tan^(-1)((1)/(x_(3))+(1)/(x_(1)))`
`=(pi)/(2)+0-(pi)/(4)=(pi)/(4)`