Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 7775 by sandy_suhendra last updated on 14/Sep/16

Commented by sou1618 last updated on 15/Sep/16

x=4−(√3) x^4 −6x^3 −2x^2 +18x+23=? (x−4+(√3))(x−4−(√3))=0 (∵x=4−(√3)) ⇒x^2 −8x+13=0 (x^4 −6x^3 −2x^2 +18x+23)÷(x^2 −8x+13) =(x^2 +2x+1)+((10)/(x^2 −8x+13)) so x^4 −6x^3 −2x^2 +18x+23=(x^2 −8x+13)(x^2 +2x+1)+10 =10

$${x}=\mathrm{4}−\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{18}{x}+\mathrm{23}=? \\ $$$$ \\ $$$$\left({x}−\mathrm{4}+\sqrt{\mathrm{3}}\right)\left({x}−\mathrm{4}−\sqrt{\mathrm{3}}\right)=\mathrm{0}\:\:\:\:\left(\because{x}=\mathrm{4}−\sqrt{\mathrm{3}}\right) \\ $$$$\Rightarrow{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{13}=\mathrm{0} \\ $$$$ \\ $$$$\left({x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{18}{x}+\mathrm{23}\right)\boldsymbol{\div}\left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{13}\right) \\ $$$$=\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}\right)+\frac{\mathrm{10}}{{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{13}} \\ $$$$ \\ $$$${so} \\ $$$${x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{18}{x}+\mathrm{23}=\left({x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{13}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}\right)+\mathrm{10} \\ $$$$=\mathrm{10} \\ $$$$ \\ $$

Commented by sandy_suhendra last updated on 15/Sep/16

Nice, thank′s for your answer

$${Nice},\:{thank}'{s}\:{for}\:{your}\:{answer} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com