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Question Number 158088 by Gbenga last updated on 31/Oct/21

$$1,2,3,4,5,\left(x\right)$$$$whatisxnotenot6$$

Commented by MJS_new last updated on 31/Oct/21

$$f\left(n\right)=\frac{x-6}{120}{n}^5-\frac{x-6}{8}{n}^4+\frac{17(x-6)}{24}{n}^3-\frac{15(x-6)}{8}{n}^2+\frac{137x-762}{60}n+6-x$$$$\mathrm{input}n=6\mathrm{and}\mathrm{the}\mathrm{desired}x$$$$\mathrm{i}.\mathrm{e}.$$$$x=5\Rightarrow f\left(n\right)=-\frac{n^5}{120}+\frac{n^4}{8}-\frac{17n^3}{24}+\frac{15n^2}{8}-\frac{77}{60}n+1$$$$x=6\Rightarrow f\left(n\right)=n$$$$x=7\Rightarrow f\left(n\right)=\frac{n^5}{120}-\frac{n^4}{8}+\frac{17n^3}{24}-\frac{15n^2}{8}+\frac{197}{60}n-1$$$$...$$

Answered by MJS_new last updated on 31/Oct/21

$$\mathrm{we}\mathrm{can}\mathrm{find}\mathrm{a}\mathrm{polynome}\mathrm{of}\mathrm{degree}5\mathrm{for}\mathrm{any}$$$$x\in \mathbb{C},\mathrm{so}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{unique}\mathrm{answer}$$

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