The number of the solutions of the equation `2 sin^(-1) sqrt(x^(2) + x + 1) + cos^(-1) sqrt(x^(2) + x) = (3pi)/(2)` is

Options

A. 0
B. `-1`
C. 1
D. 2

Answer

D

Explanation

`0 le x^(2) + x + 1 le 1 and 0 le x^(2) + x le 1`
`:. X = -1, 0`
For `x = -1`
`L.H.S. = 2 sin^(-1) 1 + cos^(-1) 0 = (3pi)/(2)`
For `x = 0, L.H.S. = 2 sin^(-1) 1 + cos^(-1) 0 = (3pi)/(2)`
Therefore, `x = 0` is a solution and sum of the solutions `= -1`