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HMMT 二月 2006 · 冲刺赛 · 第 7 题

HMMT February 2006 — Guts Round — Problem 7

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [6] Find all real numbers x such that x + + = 10 . 2 3
解析
  1. Find all real numbers x such that ⌊ ⌋ ⌊ ⌋ x x 2 x + + = 10 . 2 3 √ Answer: − 14 2 Solution: Evidently x must be an integer. Well, there aren’t that many things to √ √ check, are there? Among positive x , 8 is too small and 9 is too big; among negative √ √ x, − 15 is too small and − 13 is too big.