返回题库

HMMT 十一月 2008 · 冲刺赛 · 第 1 题

HMMT November 2008 — Guts Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 5 ] Find the sum of all solutions for x : xy = 1 x + y = 3
解析
  1. [ 5 ] Find the sum of all solutions for x : xy = 1 x + y = 3 Answer: 3 Substitute 3 − x in for y into the first equation: 2 x (3 − x ) = 1 ⇔ x − 3 x + 1 = 0 This equation has two distinct roots, each of which corresponds to a possible solution x . The sum of − b 2 the roots of the quadratic equation ax + bx + c = 0 is , which in this case is 3. a