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HMMT 二月 2003 · 冲刺赛 · 第 32 题

HMMT February 2003 — Guts Round — Problem 32

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [10] If x , y , and z are real numbers such that 2 x + y + z = 2 x − 4 y + 2 xz − 5, find the maximum possible value of x − y + z .
解析
  1. If x , y , and z are real numbers such that 2 x + y + z = 2 x − 4 y + 2 xz − 5, find the maximum possible value of x − y + z . Solution: 4 2 2 2 The equation rearranges as ( x − 1) + ( y + 2) + ( x − z ) = 0, so we must have x = 1, y = − 2, z = 1, giving us 4. 8