Question Number 147893 by mathdanisur last updated on 24/Jul/21
$${x}\:+\:\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{4}\:\:\Rightarrow\:\:{x}\:+\:\mathrm{1}\:-\:\frac{\mathrm{1}}{{x}}\:=\:? \\ $$
Commented by aliibrahim1 last updated on 24/Jul/21
$${x}+\frac{\mathrm{1}}{{x}}=\mathrm{3}\Rrightarrow\:\:\:\:\:\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} =\mathrm{3}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\mathrm{2}=\mathrm{9} \\ $$$${x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}} }−\mathrm{2}=\mathrm{5} \\ $$$$\left({x}−\frac{\mathrm{1}}{{x}}\right)^{\mathrm{2}} =\mathrm{5}\:\Rrightarrow\:\:\:\:\:{x}−\frac{\mathrm{1}}{{x}}=\sqrt{\mathrm{5}} \\ $$$${x}−\frac{\mathrm{1}}{{x}}+\mathrm{1}=\sqrt{\mathrm{5}}+\mathrm{1} \\ $$
Commented by mathdanisur last updated on 24/Jul/21
$${Thankyou}\:{Sir} \\ $$