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HMMT 二月 2007 · 代数 · 第 3 题

HMMT February 2007 — Algebra — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Three real numbers x, y , and z are such that ( x +4) / 2 = ( y +9) / ( z − 3) = ( x +5) / ( z − 5). Determine the value of x/y .
解析
  1. [ 4 ] Three real numbers x, y , and z are such that ( x +4) / 2 = ( y +9) / ( z − 3) = ( x +5) / ( z − 5). Determine the value of x/y . Answer: 1 / 2 . Because the first and third fractions are equal, adding their numerators and denomi- nators produces another fraction equal to the others: (( x + 4) + ( x + 5)) / (2 + ( z − 5)) = (2 x + 9) / ( z − 3). Then y + 9 = 2 x + 9 , etc.