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HMMT 十一月 2011 · GEN 赛 · 第 1 题

HMMT November 2011 — GEN Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Find all ordered pairs of real numbers ( x, y ) such that x y = 3 and x + xy = 4.
解析
  1. [ 3 ] Find all ordered pairs of real numbers ( x, y ) such that x y = 3 and x + xy = 4. 1 Answer: (1 , 3) , (3 , ) Multiplying the second equation by x gives 3 2 2 x + x y = 4 x, 2 and substituting our known value of x y gives the quadratic 2 x − 4 x + 3 = 0 , so x = 1 or x = 3. Hence, we obtain the solutions ( x, y ) = (1 , 3) , (3 , 1 / 3).