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Question Number 102927 by I want to learn more last updated on 11/Jul/20

$$\mathrm{If}\frac{\mathrm{x}}{{\mathrm{x}}^2+\mathrm{x}+1}=\frac{1}{4}$$$$\mathrm{Find}\mathrm{x}+\frac{1}{\mathrm{x}}$$

Commented by I want to learn more last updated on 11/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by Dwaipayan Shikari last updated on 11/Jul/20

$$\frac{x}{x^2+x+1}=\frac{1}{4}\Rightarrow \frac{1}{x+\frac{1}{x}+1}=\frac{1}{4}\Rightarrow x+\frac{1}{x}+1=4\Rightarrow x+\frac{1}{x}=3$$

Commented by I want to learn more last updated on 11/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by Rasheed.Sindhi last updated on 11/Jul/20

$$\frac{\mathrm{x}}{{\mathrm{x}}^2+\mathrm{x}+1}=\frac{1}{4},\mathrm{x}+\frac{1}{\mathrm{x}}=?$$$$\frac{1}{\frac{{\mathrm{x}}^2+\mathrm{x}+1}{\mathrm{x}}}=\frac{1}{4}$$$$\frac{1}{\mathrm{x}+\frac{1}{\mathrm{x}}+1}=\frac{1}{4}$$$$\mathrm{x}+\frac{1}{\mathrm{x}}+1=4$$$$\mathrm{x}+\frac{1}{\mathrm{x}}=3$$

Commented by I want to learn more last updated on 11/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

Answered by Rasheed.Sindhi last updated on 11/Jul/20

$$\frac{\mathrm{x}}{{\mathrm{x}}^2+\mathrm{x}+1}=\frac{1}{4}$$$$\frac{{\mathrm{x}}^2+\mathrm{x}+1}{x}=\frac{4}{1}$$$$x+\frac{1}{x}+1=4$$$$x+\frac{1}{x}=3$$

Commented by I want to learn more last updated on 11/Jul/20

$$\mathrm{Thanks}\mathrm{sir}$$

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