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Question Number 128132 by I want to learn more last updated on 04/Jan/21

$$\mathrm{If}\mathrm{f}(\mathrm{x}+\frac{1}{\mathrm{x}})={\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4},\mathrm{find}\mathrm{f}\left(5\right)$$

Answered by Olaf last updated on 04/Jan/21

$$f(x+\frac{1}{x})=x^4+\frac{1}{x^4}={(x^2+\frac{1}{x^2})}^2-2$$$$={[{(x+\frac{1}{x})}^2-2]}^2-2$$$$\mathrm{If}u=x+\frac{1}{x}$$$$f\left(u\right)={(u^2-2)}^2-2$$$$f\left(5\right)={(25-2)}^2-2=527$$

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