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HMMT 二月 2006 · 冲刺赛 · 第 7 题

HMMT February 2006 — Guts Round — Problem 7

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [6] Find all real numbers x such that x + + = 10 .
    2 3
解析

英文解析

  1. Find all real numbers x such that
    ⌊ ⌋ ⌊ ⌋
    x xx + + = 10 .2
    2 3
    √
    Answer: − 14
    Solution: Evidently x must be an integer. Well, there aren’t that many things to 2
    √ √
    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.