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Question Number 153420 by alcohol last updated on 07/Sep/21

$$howmanyx\in \mathbb{R}satisfy{x}^{99}-99x+1=0$$

Answered by mr W last updated on 07/Sep/21

$$f^{\prime }\left(x\right)=99x^{98}-99=0$$$$x=\pm 1$$$$f(-1)=-1+99+1=99$$$$f\left(1\right)=1-99+1=-97$$$$f(-\mathrm{\infty })\to -\mathrm{\infty }$$$$f(+\mathrm{\infty })\to +\mathrm{\infty }$$$$\Rightarrow threerealroots!$$

Commented by mr W last updated on 07/Sep/21

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