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x=\frac12$ ($\sqrt[3]{2+\sqrt3}+\sqrt[3]{2-\sqrt3} (HOMC 2012 Q4)

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July 24, 2019
algebrafloor functionRadicals

Problem Statement

What is the largest integer less than or equal to 4x3−3x4x^3 - 3x, where x=2+33+2−332x=\frac{\sqrt[3]{2+\sqrt3}+\sqrt[3]{2-\sqrt3}}{2} ?
(A) 11, (B) 22, (C) 33, (D) 44, (E) None of the above.
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