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HMMT 二月 2000 · GEN 赛 · 第 1 题

HMMT February 2000 — GEN Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. If a = 2 b + , b = 2 + d , 2 = d + a 1, d = a , what is b ?
    Æ Æ9
解析

英文解析

  1. Sin e d = a , substitute in to the equation b = 2 + d to get b = 2 + a = a + .
    Also, substitute in to 2 = d + a 1 to get 2 = a + a 1, or 3 = 2 a 1. No w, sin eb = a + , we an substitute in to a = 2 b + to get a = 2 a + 2 + , or a = 3 . Sin e we 1
    kno w 3 = 2 a 1 from ab o v e, we substitute in to get 3 = 6 1, or = . Th us,
    1 429
    we nd that a = , d = , and b = .
    3 9
    9 49