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2003 AMC 10AProblem 18P16-20~3 minPrint
QuadraticsAlgebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

What is the sum of the reciprocals of the roots of the equation 20032004x+1+1x=0\frac{2003}{2004}x+1+\frac{1}{x}=0 ?

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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.