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HMMT 十一月 2014 · 冲刺赛 · 第 5 题

HMMT November 2014 — Guts Round — Problem 5

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Suppose that x, y, z are real numbers such thatx = y + z + 2 , y = z + x + 1 , and z = x + y + 4 .
    Compute x + y + z .
    ° °
解析

英文解析

  1. [ 6 ] Suppose that x, y, z are real numbers such thatx = y + z + 2 , y = z + x + 1 , and z = x + y + 4 .
    Compute x + y + z .
    Answer: − 7 Adding all three equations givesx + y + z = 2( x + y + z ) + 7 ,
    from which we find that x + y + z = − 7.
    ° °