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HMMT 十一月 2023 · 团队赛 · 第 2 题

HMMT November 2023 — Team Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [20] A real number x satisfies 9 + 3 = 6 . Compute the value of 16 + 4 .
解析
  1. [20] A real number x satisfies 9 + 3 = 6. Compute the value of 16 + 4 . Proposed by: Karthik Venkata Vedula Answer: 90 x Solution: Setting y = 3 in the given equation yields 2 2 y + y = 6 = ⇒ y + y − 6 = 0 = ⇒ y = − 3 , 2 . Since y > 0 we must have x 3 = 2 = ⇒ x = log (2) = ⇒ 1 /x = log (3) . 3 2 This means that 1 /x 1 /x 1 /x 4 1 /x 2 4 2 16 + 4 = (2 ) + (2 ) = 3 + 3 = 90 .