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# Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

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Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2}+\sqrt[3]{4}$ as a root.

I've been working on this question for some time, but I haven't made any headway. Can somebody write a solution to this?

Feb 20, 2021

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Find a cubic polynomial with integer coefficients that has $$\sqrt[3]{2}+\sqrt[3]{4}$$ as a root.

The cubic polynomial is $$x^3-6x-6 = 0$$

Feb 20, 2021