作者YHank (Hank--since 2002/10)
看板tutor
标题Re: [解题] 一题多项式请高手帮忙！
时间Tue Jun 10 00:43:12 2014
※ 引述《sunfin (远方)》之铭言：
: 已知(x+y+z)(x+y)(y+z)(z+x)不等於零
: 且[x^2/(y+z)]+[y^2/(z+x)]+[z^2/(x+y)]=0
: 求:
: 1. [x/(y+z)] + [y/(z+x)] + [z/(x+y)] = ?
: 2. [x^2/(yz)] + [y^2/(zx)] + [z^2/(xy)] = ?
: 感激不尽！
1. 设答案为w，
w(x+y+z) = ......(请自行整理)
= [x^2/(y+z)]+[y^2/(z+x)]+[z^2/(x+y)]+x+y+z = x+y+z
(x+y+z)不为0，w=1
2. 已知[x/(y+z)]+[y/(z+x)]+[z/(x+y)] = 1
展开之，整理後得x^3+y^3+z^3+xyz=0
又xyz不为0，同除xyz得[x^2/(yz)]+[y^2/(zx)]+[z^2/(xy)]+1=0
所求为-1
其实我会想po是想请问第二小题是否有更elegant的解法，总觉得这样解稍嫌暴力...
--
※ 发信站: 批踢踢实业坊(ptt.cc), 来自: 61.228.244.40
※ 文章网址: http://webptt.com/cn.aspx?n=bbs/tutor/M.1402332194.A.D15.html