HMMT 二月 2007 · 代数 · 第 2 题
HMMT February 2007 — Algebra — Problem 2
题目详情
- [ 3 ] Two reals x and y are such that x − y = 4 and x − y = 28. Compute xy .
解析
- [ 3 ] Two reals x and y are such that x − y = 4 and x − y = 28. Compute xy . 3 3 2 2 2 Answer: − 3 . We have 28 = x − y = ( x − y )( x + xy + y ) = ( x − y )(( x − y ) + 3 xy ) = 4 · (16 + 3 xy ), from which xy = − 3.