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2020 AMC 10AProblem 14P11-15~5 minPrint
Algebraic ManipulationQuadraticsApply an identity: SFFT, sum of squares, difference of cubes, Vieta

Real numbers xx and yy satisfy x+y=4x + y = 4 and x⋅y=−2x \cdot y = -2 . What is the value of x+x3y2+y3x2+y?x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?

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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.