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2007 AMC 10AProblem 20P16-20~2 minPrint
Algebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, Vieta

Suppose that the number aa satisfies the equation 4=a+a−14 = a + a^{ - 1} . What is the value of a4+a−4a^{4} + a^{ - 4} ?

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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.