Question Number 102927 by I want to learn more last updated on 11/Jul/20
$$\mathrm{If}\:\:\:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} \:\:+\:\:\mathrm{x}\:\:+\:\:\mathrm{1}}\:\:\:=\:\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{Find}\:\:\:\:\:\mathrm{x}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$
Commented by I want to learn more last updated on 11/Jul/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$
Answered by Dwaipayan Shikari last updated on 11/Jul/20
$$\frac{{x}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{4}}\Rightarrow\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{{x}}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{4}}\Rightarrow{x}+\frac{\mathrm{1}}{{x}}+\mathrm{1}=\mathrm{4}\:\:\Rightarrow{x}+\frac{\mathrm{1}}{{x}}=\mathrm{3} \\ $$
Commented by I want to learn more last updated on 11/Jul/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$
Answered by Rasheed.Sindhi last updated on 11/Jul/20
$$\:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{4}}\:\:,\:\:\mathrm{x}+\:\frac{\mathrm{1}}{\mathrm{x}}=? \\ $$$$\frac{\mathrm{1}}{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}{\mathrm{x}}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{1}=\mathrm{4} \\ $$$$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{3}\: \\ $$
Commented by I want to learn more last updated on 11/Jul/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$
Answered by Rasheed.Sindhi last updated on 11/Jul/20
$$\:\frac{\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}{{x}}=\frac{\mathrm{4}}{\mathrm{1}} \\ $$$${x}+\frac{\mathrm{1}}{{x}}+\mathrm{1}=\mathrm{4} \\ $$$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3} \\ $$
Commented by I want to learn more last updated on 11/Jul/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$