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Question Number 14658 by tawa tawa last updated on 03/Jun/17

$$\mathrm{Given}\mathrm{that}:$$$$\mathrm{x}={(\sqrt{2}+1)}^{1/3}-{(\sqrt{2}-1)}^{1/3}$$$$\mathrm{Show}\mathrm{that},{\mathrm{x}}^3+3\mathrm{x}=2$$

Answered by Tinkutara last updated on 03/Jun/17

$$x^3=\sqrt{2}+1-\sqrt{2}+1-3\left(1\right)\left(x\right)$$$$[\mathrm{Using}{(a-b)}^3=a^3-b^3-3ab(a-b)]$$$$x^3+3x=2$$

Commented by tawa tawa last updated on 03/Jun/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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