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Question Number 84588 by john santu last updated on 14/Mar/20

$$\mathrm{if}\mathrm{x}-\frac{1}{\mathrm{x}}=9$$$${\mathrm{x}}^3-\frac{1}{{\mathrm{x}}^3}=?$$

Answered by john santu last updated on 14/Mar/20

Answered by nimnim last updated on 14/Mar/20

$${(x-\frac{1}{x})}^3={\left(9\right)}^3$$$$\Rightarrow {\left(x\right)}^3-{\left(\frac{1}{x}\right)}^3-3\left(x\right)\left(\frac{1}{x}\right)(x-\frac{1}{x})=729$$$$\Rightarrow x^3-\frac{1}{x^3}-3\left(9\right)=729$$$$\Rightarrow x^3-\frac{1}{x^3}=729+27$$$$\Rightarrow x^3-\frac{1}{x^3}=756$$

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