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Question Number 159034 by HongKing last updated on 12/Nov/21

Answered by mindispower last updated on 12/Nov/21

$$a=\sqrt[n]{\frac{11+x}{11-x}},b=\sqrt{\frac{2021+x}{2021-x}}$$$$a+\frac{1}{a}=b+\frac{1}{b}$$$$(a-b)(1-\frac{1}{ab})=0$$$$a=b,ab=1$$$$a=b\Rightarrow \frac{11+x}{11-x}=\frac{2021+x}{2021-x},x=0$$$$ab=1\Rightarrow (11+x)(2021-x)=(2021+x)(11-x)$$$$\Rightarrow 2010x=-2010x\Rightarrow x=0$$$$S=\left\{0\right\}$$$$$$$$$$$$$$

Commented by HongKing last updated on 12/Nov/21

$$\mathrm{Cool}\mathrm{my}\mathrm{dear}\mathrm{Ser}\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}$$

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