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

If   (x/(x^2   +  x  +  1))   =  (1/4)  Find     x  +  (1/x)

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

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

Thanks sir

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

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

(x/(x^2 +x+1))=(1/4)⇒(1/(x+(1/x)+1))=(1/4)⇒x+(1/x)+1=4  ⇒x+(1/x)=3

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

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

Thanks sir

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

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

 (x/(x^2 +x+1))=(1/4)  ,  x+ (1/x)=?  (1/((x^2 +x+1)/x))=(1/4)  (1/(x+(1/x)+1))=(1/4)  x+(1/x)+1=4  x+(1/x)=3

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

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

Thanks sir

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

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

 (x/(x^2 +x+1))= (1/4)  ((x^2 +x+1)/x)=(4/1)  x+(1/x)+1=4  x+(1/x)=3

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

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

Thanks sir

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

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