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HMMT 二月 2008 · 冲刺赛 · 第 4 题

HMMT February 2008 — Guts Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Find the real solution(s) to the equation ( x + y ) = ( x + 1)( y − 1).
解析
  1. [ 6 ] Find the real solution(s) to the equation ( x + y ) = ( x + 1)( y − 1). 2 Answer: ( − 1 , 1) Set p = x + 1 and q = y − 1, then we get ( p + q ) = pq , which simplifies to 2 q 3 q 2 2 2 p + pq + q = 0. Then we have ( p + ) + , and so p = q = 0. Thus ( x, y ) = ( − 1 , 1). 2 4