HMMT 二月 2003 · 代数 · 第 1 题
HMMT February 2003 — Algebra — Problem 1
题目详情
英文原题
- Find the smallest value of x such that a ≥ 14 a − x for all nonnegative a .
2 ° °2
tan (20 ) − sin (20 )
解析
英文解析
- 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
√ √
just the maximum possible value of 14 a − a = 49 − ( a − 7) , which is clearly 49,2
achieved when a = 49.
2 ° °2
tan (20 ) − sin (20 )