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Question Number 87033 by Zainal Arifin last updated on 02/Apr/20

Find the value of x^3 + (1/x^3 )   ,   when     x + (1/x) = 5

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:\:\:,\:\:\:\mathrm{when} \\ $$$$\:\:\:{x}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5} \\ $$

Answered by redmiiuser last updated on 02/Apr/20

(x+(1/x))^3 =125  ⇒x^3 +(1/x^3 )+3(x+(1/x))=125  x^3 +(1/x^3 )=125−15=110

$$\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} =\mathrm{125} \\ $$$$\Rightarrow{x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{3}\left({x}+\frac{\mathrm{1}}{{x}}\right)=\mathrm{125} \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{125}−\mathrm{15}=\mathrm{110} \\ $$

Commented by Zainal Arifin last updated on 02/Apr/20

thank you sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

Commented by redmiiuser last updated on 02/Apr/20

welcome

$${welcome}\: \\ $$

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