返回题库

HMMT 二月 2009 · GEN1 赛 · 第 8 题

HMMT February 2009 — GEN1 Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] Let a , b , and c be the 3 roots of x − x + 1 = 0. Find + + .
    a +1 b +1 c +1
解析

英文解析

  1. [ 5 ] Let a , b , and c be the 3 roots of x − x + 1 = 0. Find + + .
    a +1 b +1 c +1
    Answer: − 2
    Solution: We can substitute x = y − 1 to obtain a polynomial having roots a + 1, b + 1, c + 1, namely,
    3 3 2
    ( y − 1) − ( y − 1) + 1 = y − 3 y + 2 y + 1. The sum of the reciprocals of the roots of this polynomialis, by Viete’s formulas, = − 2.2 − 1