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2006 AMC 10BProblem 14P11-15~3 minPrint
QuadraticsAlgebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, Vieta

Let aa and bb be the roots of the equation x2−mx+2=0x^2-mx+2=0 . Suppose that a+1ba+\frac1b and b+1ab+\frac1a are the roots of the equation x2−px+q=0x^2-px+q=0 . What is qq ?

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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.