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HMMT 二月 2008 · GEN1 赛 · 第 7 题

HMMT February 2008 — GEN1 Round — Problem 7

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 5 ] The equation x − 9 x + 8 x + 2 = 0 has three real roots p , q , r . Find + + . 2 2 2 p q r
解析
  1. [ 5 ] The equation x − 9 x + 8 x + 2 = 0 has three real roots p , q , r . Find + + . 2 2 2 p q r Answer: 25 From Vieta’s relations, we have p + q + r = 9, pq + qr + pr = 8 and pqr = − 2. So 2 2 1 1 1 ( pq + qr + rp ) − 2( p + q + r )( pqr ) 8 − 2 · 9 · ( − 2)
    • = = = 25 . 2 2 2 2 2 p q r ( pqr ) ( − 2)