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Approximation of Cube Root of 2

Source: 1972 USAMO Problem 4

March 6, 2010
geometry3D geometryinequalities

Problem Statement

Let R R denote a non-negative rational number. Determine a fixed set of integers a,b,c,d,e,f a,b,c,d,e,f, such that for every choice of R R, \left| \frac{aR^2\plus{}bR\plus{}c}{dR^2\plus{}eR\plus{}f}\minus{}\sqrt[3]{2}\right| < \left|R\minus{}\sqrt[3]{2}\right|.
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