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Question Number 80243 by mr W last updated on 01/Feb/20

$$ifx+\frac{1}{x}=a(a\in \mathbb{R})$$$$find{x}^n+\frac{1}{x^n}=?$$$$(n\in \mathbb{N})$$

Commented by TawaTawa last updated on 01/Feb/20

$$\mathrm{Sir}\mathrm{i}\mathrm{thought}\mathrm{you}\mathrm{solved}\mathrm{this}\mathrm{before}\mathrm{with}\mathrm{sir}\mathrm{mind}\mathrm{is}\mathrm{power}$$$$\mathrm{Q}78931$$

Commented by TawaTawa last updated on 01/Feb/20

$$\mathrm{Or}\mathrm{you}\mathrm{have}\mathrm{another}\mathrm{way}\mathrm{sir}$$

Commented by TawaTawa last updated on 01/Feb/20

$$\mathrm{Or}\mathrm{you}\mathrm{have}\mathrm{another}\mathrm{way}\mathrm{sir}$$

Commented by behi83417@gmail.com last updated on 01/Feb/20

$$\mathrm{sir}\mathrm{mrW}!\mathrm{what}\mathrm{do}\mathrm{think}\mathrm{about}\mathrm{this}?$$$${\mathbf{a}}^{\mathbf{n}}+{\mathbf{b}}^{\mathbf{n}}={(\mathbf{a}+\mathbf{b})}^{\mathbf{n}}-\mathbf{nab}{(\mathbf{a}+\mathbf{b})}^{\mathbf{n}-2}[\mathbf{n}⩾2]$$

Commented by behi83417@gmail.com last updated on 01/Feb/20

$$\mathrm{i}\mathrm{mean}\mathrm{that}:\mathrm{is}\mathrm{this}\mathrm{true}?\mathrm{or}\mathrm{can}\mathrm{we}\mathrm{prove}$$$$\mathrm{it}?$$

Commented by mr W last updated on 01/Feb/20

$$nosir,$$$${\mathbf{a}}^{\mathbf{n}}+{\mathbf{b}}^{\mathbf{n}}={(\mathbf{a}+\mathbf{b})}^{\mathbf{n}}-\mathbf{nab}{(\mathbf{a}+\mathbf{b})}^{\mathbf{n}-2}[\mathbf{n}⩾2]$$$$isnottrue.$$

Commented by behi83417@gmail.com last updated on 01/Feb/20

$${\mathrm{a}}^2+{\mathrm{b}}^2={(\mathrm{a}+\mathrm{b})}^2-2\mathrm{ab}{(\mathrm{a}+\mathrm{b})}^0$$$${\mathrm{a}}^3+{\mathrm{b}}^3={(\mathrm{a}+\mathrm{b})}^3-3\mathrm{ab}{(\mathrm{a}+\mathrm{b})}^1$$$$.....$$

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