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 122174 by AbdullahMohammadNurusSafa last updated on 14/Nov/20

If  x = (√(5 )) + (√3),then x^3  + (1/x^3 ) = ?  or, is it possible at all?

$${If}\:\:\boldsymbol{{x}}\:=\:\sqrt{\mathrm{5}\:}\:+\:\sqrt{\mathrm{3}},{then}\:\boldsymbol{{x}}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:? \\ $$$$\boldsymbol{{or}},\:\boldsymbol{{is}}\:\boldsymbol{{it}}\:\boldsymbol{{possible}}\:\boldsymbol{{at}}\:\boldsymbol{{all}}? \\ $$

Answered by behi83417@gmail.com last updated on 14/Nov/20

x^3 +(1/x^3 )=(x+(1/x))^3 −3(x+(1/x))=  =(5(√5)+3(√3)+15(√3)+27(√5))−3((√5)+(√3))=  =29(√5)+15(√3) .

$$\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }=\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{3}} −\mathrm{3}\left(\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\right)= \\ $$$$=\left(\mathrm{5}\sqrt{\mathrm{5}}+\mathrm{3}\sqrt{\mathrm{3}}+\mathrm{15}\sqrt{\mathrm{3}}+\mathrm{27}\sqrt{\mathrm{5}}\right)−\mathrm{3}\left(\sqrt{\mathrm{5}}+\sqrt{\mathrm{3}}\right)= \\ $$$$=\mathrm{29}\sqrt{\mathrm{5}}+\mathrm{15}\sqrt{\mathrm{3}}\:. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com