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HMMT 十一月 2008 · 冲刺赛 · 第 1 题

HMMT November 2008 — Guts Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] Find the sum of all solutions for x :
    xy = 1
    x + y = 3
解析

英文解析

  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:
    x (3 − x ) = 1 ⇔ x − 3 x + 1 = 02
    This equation has two distinct roots, each of which corresponds to a possible solution x . The sum of − bthe roots of the quadratic equation ax + bx + c = 0 is , which in this case is 3.2 a