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Number of real solutions of tan^-1 sqrt(x(x+1)) + sin^-1 sqrt(x^2+x+1) = pi/2

The same question, asked 2 times: 2 May 2023 S1, 3 May 2023 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S1

    123
    The number of real solutions of tan⁡−1x(x+1)+sin⁡−1x2+x+1=π2\tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2+x+1} = \dfrac{\pi}{2} is

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  2. Question 2

    3 May 2023 S1

    115
    The number of real solutions of tan⁡−1 ⁣x(x+1)+sin⁡−1 ⁣x2+x+1=π2\tan^{-1}\!\sqrt{x(x+1)}+\sin^{-1}\!\sqrt{x^2+x+1}=\frac{\pi}{2} is

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