The number of real roots of the equation { an ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4} is :

Question

The number of real roots of the equation {	an ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4} is :

Accepted Answer

Answer: D. 0 {	an ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4} For equation to be defined, x2 + x \ge 0 \Rightarrow x2 + x + 1 \ge 1 	herefore Only possibility that the equation is defined x2 + x = 0 \Rightarrow x = 0; x = -1 None of these values satisfy 	herefore No of roots = 0

The number of real roots of the equation $${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4}$$ is :

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