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Question-7775




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

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