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2011 AMC 10BProblem 19P16-20~3 minPrint
Absolute Value & InequalitiesQuadraticsSubstitute to simplify (u = x+1/x, shifting, scaling)Exploit symmetry to reduce work or pair up objects

What is the product of all the roots of the equation 5∣x∣+8=x2−16.\sqrt{5 | x | + 8} = \sqrt{x^2 - 16}.

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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.