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Question-211402




Question Number 211402 by efronzo1 last updated on 08/Sep/24
Answered by A5T last updated on 08/Sep/24
Q211029, we can find a polynomial f(x)  f(x)=x^n +_− 1  f(3)=28⇒f(x)=x^3 +1  (x^3 +1)((1/x^3 )+1)=(x^3 +1)+((1/x^3 )+1)  ⇒f(−2)+f(−(1/2))=−(6(1/8))=−((49)/8)
$${Q}\mathrm{211029},\:{we}\:{can}\:{find}\:{a}\:{polynomial}\:{f}\left({x}\right) \\ $$$${f}\left({x}\right)={x}^{{n}} \underset{−} {+}\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{28}\Rightarrow{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1} \\ $$$$\left({x}^{\mathrm{3}} +\mathrm{1}\right)\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{1}\right)=\left({x}^{\mathrm{3}} +\mathrm{1}\right)+\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\mathrm{1}\right) \\ $$$$\Rightarrow{f}\left(−\mathrm{2}\right)+{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=−\left(\mathrm{6}\frac{\mathrm{1}}{\mathrm{8}}\right)=−\frac{\mathrm{49}}{\mathrm{8}} \\ $$

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