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The number of real solutions of the equa...

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