AMC 10 Step by Step
Log inSign up
2018 AMC 10BProblem 25P21-25~10 minPrint
Number PropertiesFunctionsQuadraticsBound the quantity above/below or estimate to pin it downSubstitute to simplify (u = x+1/x, shifting, scaling)

Let ⌊x⌋\lfloor x \rfloor denote the greatest integer less than or equal to xx . How many real numbers xx satisfy the equation x2+10,000⌊x⌋=10,000xx^2 + 10,000\lfloor x \rfloor = 10,000x ?

Log in to save your progress.

Similar problems

Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.