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HMMT 十一月 2012 · 冲刺赛 · 第 5 题

HMMT November 2012 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] a and b are complex numbers such that 2 a + 3 b = 10 and 4 a + 9 b = 20. Find ab .
解析
  1. [ 6 ] 20 Answer: 3 2 2 20 = 4 a + 9 b 2 2 20 + 12 ab = 4 a + 12 ab + 9 b 2 20 + 12 ab = (2 a + 3 b ) 20 + 12 ab = 100 12 ab = 80 20 ab = 3