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2000 AMC 10Problem 24P21-25~5 minPrint
FunctionsQuadraticsApply an identity: SFFT, sum of squares, difference of cubes, VietaSubstitute to simplify (u = x+1/x, shifting, scaling)

Let ff be a function for which f(x3)=x2+x+1f\left(\dfrac{x}{3}\right) = x^2 + x + 1 . Find the sum of all values of zz for which f(3z)=7f(3z) = 7 .

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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. Also appeared as 2000 12 #15.