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Question Number 195083 by sciencestudentW last updated on 23/Jul/23

$$x=\sqrt{5}-2$$$$x+\frac{1}{x}=?$$

Answered by Rasheed.Sindhi last updated on 23/Jul/23

$$x=\sqrt{5}-2,x+\frac{1}{x}=?$$$$\frac{1}{x}=\frac{1}{\sqrt{5}-2}=\frac{1}{\sqrt{5}-2}\cdot \frac{\sqrt{5}+2}{\sqrt{5}+2}$$$$=\frac{\sqrt{5}+2}{5-4}=\sqrt{5}+2$$$$x+\frac{1}{x}=(\sqrt{5}-2)+(\sqrt{5}+2)=2\sqrt{5}$$

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