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Question Number 122174 by AbdullahMohammadNurusSafa last updated on 14/Nov/20

$$If\mathit{x}=\sqrt{5}+\sqrt{3},then{\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}=?$$$$\mathit{o}\mathit{r},\mathit{i}\mathit{s}\mathit{i}\mathit{t}\mathit{p}\mathit{o}\mathit{s}\mathit{s}\mathit{i}\mathit{b}\mathit{l}\mathit{e}\mathit{a}\mathit{t}\mathit{a}\mathit{l}\mathit{l}?$$

Answered by behi83417@gmail.com last updated on 14/Nov/20

$${\mathrm{x}}^3+\frac{1}{{\mathrm{x}}^3}={(\mathrm{x}+\frac{1}{\mathrm{x}})}^3-3(\mathrm{x}+\frac{1}{\mathrm{x}})=$$$$=(5\sqrt{5}+3\sqrt{3}+15\sqrt{3}+27\sqrt{5})-3(\sqrt{5}+\sqrt{3})=$$$$=29\sqrt{5}+15\sqrt{3}.$$

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