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2012 AMC 10AProblem 17P16-20~5 minPrint
Algebraic ManipulationDiophantine EquationsDivisibility & FactorsApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

Let aa and bb be relatively prime positive integers with a>b>0a>b>0 and a3−b3(a−b)3=733\dfrac{a^3-b^3}{(a-b)^3} = \dfrac{73}{3} . What is a−ba-b ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.