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The sum of the solution of the equation ...

The sum of the solution of the equation `2sin^(-1)sqrt(x^2+x+1)+cos^(-1)sqrt(x^2+x)=(3pi)/2` is (a)0 (b) `-1` (c) `1` (d) 2

A

0

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`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`
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