Question Number 87033 by Zainal Arifin last updated on 02/Apr/20
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\:\:,\:\:\:\mathrm{when} \\ $$$$\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5} \\ $$
Answered by redmiiuser last updated on 02/Apr/20
$$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} =\mathrm{125} \\ $$$$\Rightarrow{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)=\mathrm{125} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{125}−\mathrm{15}=\mathrm{110} \\ $$
Commented by Zainal Arifin last updated on 02/Apr/20
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$
Commented by redmiiuser last updated on 02/Apr/20
$${welcome}\: \\ $$