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Denesting of Ramanujan's radicals (2)

Algebra Level 4

For what real value $k$ does

$\large \sqrt[3]{\sqrt[3]{2}-1} = \sqrt[3]{\frac{1}{9}} - \sqrt[3]{\frac{k}{9}} + \sqrt[3]{\frac{k^2}{9}}?$

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by Tommy Li

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