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

The number of the solutions of the equation `2 sin^(-1) sqrt(x^(2) + x

1.	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
Answer» Correct Answer - B `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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