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Question Number 194021 by mr W last updated on 26/Jun/23

$$find\sqrt[3]{1+\sqrt[3]{2}+\sqrt[3]{4}}=?$$

Commented by BaliramKumar last updated on 26/Jun/23

$${(2^{\frac{1}{3}}-1)}^{-\frac{1}{3}}$$

Answered by Skabetix last updated on 26/Jun/23

$$={({\left(2\right)}^{\frac{1}{3}}+{\left(4\right)}^{\frac{1}{3}}+1)}^{\frac{1}{3}}\approx 1.57$$

Answered by witcher3 last updated on 26/Jun/23

$$\mathrm{x}=\sqrt[3]{2}$$$$1+\mathrm{x}+{\mathrm{x}}^2=\frac{{\mathrm{x}}^3-1}{\mathrm{x}-1}=\frac{1}{\mathrm{x}-1}$$$$=\frac{1}{\sqrt[3]{2^{\frac{1}{3}}-1}}$$$$$$

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