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HMMT 二月 2010 · 冲刺赛 · 第 2 题

HMMT February 2010 — Guts Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 4 ] Suppose that x , y , and z are non-negative real numbers such that x + y + z = 1. What is the
    2 3
    maximum possible value of x + y + z ?
解析

英文解析

  1. [ 4 ] Suppose that x , y , and z are non-negative real numbers such that x + y + z = 1. What is the
    2 3
    maximum possible value of x + y + z ?
    2 3 2 3
    Answer: 1 Since 0 ≤ y, z ≤ 1, we have y ≤ y and z ≤ z . Therefore x + y + z ≤ x + y + z = 1.
    2 3
    We can get x + y + z = 1 by setting ( x, y, z ) = (1 , 0 , 0).