QJEEM21Ma2fa9: JEE Main 2021 Mathematics - Class 12 JEEM21Ma2fa9 Solution: The number of real roots of the equation tan − 1 x ( x + 1 ) +…

Question

Verified Solution • 2025–26 Session moderate

The number of real roots of the equation

\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{4}

is :

Accepted Answer

\tan^{- 1} \sqrt{x (x + 1)} + \sin^{- 1} \sqrt{x^{2} + x + 1} = \frac{π}{4}

For equation to be defined,

x² + x

\geq

0

\Rightarrow

x² + x + 1

\geq

1

∴

Only possibility that the equation is defined

x² + x = 0

\Rightarrow

x = 0; x =

-

1

None of these values satisfy

∴

No of roots = 0

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