If is the greatest integer less than or equal to and is the least integer greater…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

If [x][x] is the greatest integer less than or equal to xx and (x)(x) is the least integer greater than or equal to xx, and [x]2+(x)2>25[x]^2+(x)^2>25, then xx belongs to (1) [3,4][3,4] (2) (−∞,−4](-\infty,-4] (3) [4,∞)[4,\infty) (4) (−∞,−4]∪[4,∞)(-\infty,-4]\cup[4,\infty)

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