返回题库

HMMT 二月 2002 · ADV 赛 · 第 9 题

HMMT February 2002 — ADV Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Given that a, b, c are positive real numbers and log b + log c + log a = 0, find the value a b c 3 3 3 of (log b ) + (log c ) + (log a ) . a b c
解析
  1. Given that a, b, c are positive real numbers and log b + log c + log a = 0, find the a b c 3 3 3 value of (log b ) + (log c ) + (log a ) . a b c Solution: 3 . Let x = log b and y = log c ; then log a = − ( x + y ). Thus we want to a b c 3 3 3 2 2 compute the value of x + y − ( x + y ) = − 3 x y − 3 xy = − 3 xy ( x + y ). On the other hand, − xy ( x + y ) = (log b )(log c )(log a ) = 1, so the answer is 3. a b c