Question

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

• A. 1
• B. 2
• C. 4
• D. 0

Answer 1

Answer: (D)

$\tan ^{-1} \sqrt{x(x+1)}+\sin ^{-1} \sqrt{x^{2}+x+1}=\frac{\pi}{4}$
For equation to be defined,
$x^{2}+x \geq 0$
$\Rightarrow x^{2}+x+1 \geq 1$
$\therefore $ only possibility that the equation is defined
$x^{2}+x=0 \Rightarrow x=0 ; x=-1$
None of these values satisfy
$\therefore $ No of roots $=0$