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8x^3 +6x - 1, x=1/2(\sqrt[3]{2+\sqrt5}+\sqrt[3]{2-\sqrt5}) (HOMC 2013 Q3)

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July 30, 2019
floor functionpolynomialalgebra

Problem Statement

What is the largest integer not exceeding 8x3+6x−18x^3 +6x - 1, where x=12(2+53+2−53)x =\frac12 \left(\sqrt[3]{2+\sqrt5} + \sqrt[3]{2-\sqrt5}\right) ?
(A): 11, (B): 22, (C): 33, (D): 44, (E) None of the above.
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