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Category: Operation Research

let-x-y-z-be-a-complex-numbers-as-x-y-z-1-x-y-z-1-xyz-1-calcul-1-x-1-y-1-z-x-y-z-please-i-need-a-help-

Question Number 107320 by pticantor last updated on 10/Aug/20 $${let}\:{x},{y},{z}\:{be}\:{a}\:{complex}\:{numbers} \\ $$$${as}\:\mid{x}\mid=\mid{y}\mid=\mid{z}\mid=\mathrm{1} \\ $$$$\begin{cases}{{x}+{y}+{z}=\mathrm{1}}\\{{xyz}=\mathrm{1}}\end{cases} \\ $$$${calcul}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}+\frac{\mathrm{1}}{{z}}=? \\ $$$$\:\:{x}=?\:{y}=?\:{z}=? \\ $$$${please}\:{i}\:{need}\:{a}\:{help} \\ $$ Commented by bemath…

1-1-5-9-7-27-9-81-11-243-

Question Number 106860 by Dwaipayan Shikari last updated on 07/Aug/20 $$\mathrm{1}−\mathrm{1}+\frac{\mathrm{5}}{\mathrm{9}}−\frac{\mathrm{7}}{\mathrm{27}}+\frac{\mathrm{9}}{\mathrm{81}}−\frac{\mathrm{11}}{\mathrm{243}}+….. \\ $$ Commented by Dwaipayan Shikari last updated on 07/Aug/20 $$\mathrm{1}−\frac{\mathrm{3}}{\mathrm{3}}+\frac{\mathrm{5}}{\mathrm{9}}−\frac{\mathrm{7}}{\mathrm{27}}+\frac{\mathrm{9}}{\mathrm{81}}−\frac{\mathrm{11}}{\mathrm{243}}+.. \\ $$$${S}=\mathrm{1}−\mathrm{3}{x}+\mathrm{5}{x}^{\mathrm{2}} −\mathrm{7}{x}^{\mathrm{3}}…