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HMMT 十一月 2017 · 冲刺赛 · 第 14 题

HMMT November 2017 — Guts Round — Problem 14

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 5 ] Points A , B , C , and D lie on a line in that order such that = . If AC = 3 and BD = 4, BC CD find AD . 1
解析
  1. [ 5 ] Points A , B , C , and D lie on a line in that order such that = . If AC = 3 and BD = 4, BC CD find AD . Proposed by: Yuan Yao Answer: 6 3 − x 7 − x Let BC = x , then the equation becomes = . This simplifies to a quadratic equation with x 4 − x solutions x = 1 and x = 6. Since x < 3, we have x = 1 and AD = 7 − x = 6. 1