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HMMT 十一月 2022 · THM 赛 · 第 2 题

HMMT November 2022 — THM Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Alice is thinking of a positive real number x , and Bob is thinking of a positive real number y . Given √ √ y y that x = 27 and ( x ) = 9, compute xy .
解析
  1. Alice is thinking of a positive real number x , and Bob is thinking of a positive real number y . Given √ √ y y that x = 27 and ( x ) = 9, compute xy . Proposed by: Sean Li √ 4 Answer: 16 3 Solution: Note that √ √ √ √ y y y y 2 y 27 = ( x ) = x = ( x ) = 81 , √ √ √ √ 4 4 4 4 / 3 so y = 4 / 3 or y = 16 / 9. It follows that x = 27 or x = 9 3. The final answer is 9 3 · 16 / 9 = 16 3.