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Question Number 186739 by Davidtim last updated on 09/Feb/23

$$\sqrt[3]{5+\sqrt[3]{5+\sqrt[3]{5+...}}}=?$$

Answered by pablo1234523 last updated on 09/Feb/23

$$x=\sqrt[3]{5+\sqrt[3]{5+\sqrt[3]{5+...}}}$$$$\Rightarrow x=\sqrt[3]{5+x}$$$$\Rightarrow x^3-x-5=0$$$$\Rightarrow x\approx 1.9042\left(realsolution\right)$$

Commented by Frix last updated on 09/Feb/23

$$x=\sqrt[3]{\frac{5}{2}-\frac{\sqrt{2013}}{18}}+\sqrt[3]{\frac{5}{2}+\frac{\sqrt{2013}}{18}}$$

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