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Question Number 143427 by bramlexs22 last updated on 14/Jun/21

$$iff\left(x\right)ispolynomialsatisfying$$$$f\left(x\right)f\left(\frac{1}{x}\right)-2f\left(x\right)+2f\left(\frac{1}{x}\right)=5$$$$andf\left(2\right)=14thenf\left(3\right)=?$$

Answered by qaz last updated on 14/Jun/21

$$\{\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)-2\mathrm{f}\left(\mathrm{x}\right)+2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=5.......\left(1\right)\\ \mathrm{f}\left(\frac{1}{\mathrm{x}}\right)\mathrm{f}\left(\mathrm{x}\right)-2\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)+2\mathrm{f}\left(\mathrm{x}\right)=5.......\left(2\right)\end{array}$$$$\left(2\right)-\left(1\right)::$$$$\Rightarrow \mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\frac{1}{\mathrm{x}}\right)=\pm \sqrt{5}$$$$\mathrm{how}\mathrm{is}\mathrm{f}\left(2\right)=14\mathrm{this}\mathrm{possible}?$$

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