HMMT 十一月 2011 · GEN 赛 · 第 1 题

英文解析

1. [ 3 ] Find all ordered pairs of real numbers ( x, y ) such that x y = 3 and x + xy = 4.
   Answer: (1 , 3) , (3 , ) Multiplying the second equation by x gives 1
   2 23
   x + x y = 4 x,
   and substituting our known value of x y gives the quadratic 2
   x − 4 x + 3 = 0 ,2
   so x = 1 or x = 3. Hence, we obtain the solutions ( x, y ) = (1 , 3) , (3 , 1 / 3).