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2013 AMC 10BProblem 14P11-15~3 minPrint
Algebraic ManipulationCoordinate GeometryApply an identity: SFFT, sum of squares, difference of cubes, Vieta

Define a♣b=a2b−ab2a\clubsuit b=a^2b-ab^2 . Which of the following describes the set of points (x,y)(x, y) for which x♣y=y♣xx\clubsuit y=y\clubsuit x ?

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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.