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HMMT 二月 2006 · GEN2 赛 · 第 5 题

HMMT February 2006 — GEN2 Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. If a , b are nonzero real numbers such that a + b = 8 ab , find the value of . ∣ ∣ a − b
解析
  1. If a , b are nonzero real numbers such that a + b = 8 ab , find the value of . ∣ ∣ a − b √ 15 Answer: 3 Solution: Note that √ √ √ √ ∣ ∣ 2 2 2 ∣ ∣ a + b ( a + b ) a + b + 2 ab 10 ab 15 ∣ ∣ = = = = . ∣ ∣ 2 2 2 a − b ( a − b ) a + b − 2 ab 6 ab 3