Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 84588 by john santu last updated on 14/Mar/20

if x − (1/x) = 9 x^3 −(1/x^3 ) = ?

$$\mathrm{if}\:\mathrm{x}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{9} \\ $$$$\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$

Answered by john santu last updated on 14/Mar/20

Answered by nimnim last updated on 14/Mar/20

(x−(1/x))^3 =(9)^3 ⇒(x)^3 −((1/x))^3 −3(x)((1/x))(x−(1/x))=729 ⇒x^3 −(1/x^3 )−3(9)=729 ⇒ x^3 −(1/x^3 )=729+27 ⇒ x^3 −(1/x^3 )=756

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({x}−\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} =\left(\mathrm{9}\right)^{\mathrm{3}} \\ $$$$\Rightarrow\left({x}\right)^{\mathrm{3}} −\left(\frac{\mathrm{1}}{{x}}\right)^{\mathrm{3}} −\mathrm{3}\left({x}\right)\left(\frac{\mathrm{1}}{{x}}\right)\left({x}−\frac{\mathrm{1}}{{x}}\right)=\mathrm{729} \\ $$$$\Rightarrow{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}^{\mathrm{3}} }−\mathrm{3}\left(\mathrm{9}\right)=\mathrm{729} \\ $$$$\Rightarrow\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{729}+\mathrm{27} \\ $$$$\Rightarrow\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}^{\mathrm{3}} }=\mathrm{756} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com