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HMMT 二月 2002 · 冲刺赛 · 第 56 题

HMMT February 2002 — Guts Round — Problem 56

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ ± 6] x, y are positive real numbers such that x + y = xy . What is the smallest possible value of x ?
解析
  1. x, y are positive real numbers such that x + y = xy . What is the smallest possible value of x ? 2 Solution: 4 Notice that x = y / ( y − 1) = 2+( y − 1)+1 / ( y − 1) ≥ 2+2 = 4. Conversely, x = 4 is achievable, by taking y = 2.