USAMO 1972 Problem 4

Let $k$ be the real cube root of 2. Find integers A, B, C, a, b, c such that $\left|\left(A x^{2}+B x+C\right) /\left(a x^{2}+b x+c\right)-k\right|<\mid$ $\mathrm{x}-\mathrm{k} \mid$ for all non-negative rational $\mathrm{x}$.