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2002 AMC 10BProblem 20P16-20~5 minPrint
Algebraic ManipulationApply an identity: SFFT, sum of squares, difference of cubes, VietaTest small/specific values or special cases to find or verify the answer

Let aa , bb , and cc be real numbers such that a−7b+8c=4a-7b+8c=4 and 8a+4b−c=78a+4b-c=7 . Then a2−b2+c2a^2-b^2+c^2 is

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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.