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HMMT 二月 2003 · 代数 · 第 1 题

HMMT February 2003 — Algebra — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find the smallest value of x such that a ≥ 14 a − x for all nonnegative a . 2 2 ◦ ◦ tan (20 ) − sin (20 )
解析
  1. Find the smallest value of x such that a ≥ 14 a − x for all nonnegative a . Solution: 49 We want to find the smallest value of x such that x ≥ 14 sqrta − a for all a . This is √ √ 2 just the maximum possible value of 14 a − a = 49 − ( a − 7) , which is clearly 49, achieved when a = 49. 2 2 ◦ ◦ tan (20 ) − sin (20 )