HMMT 二月 2010 · 冲刺赛 · 第 2 题
HMMT February 2010 — Guts Round — Problem 2
题目详情
- [ 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
- [ 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).