※ 引述《sunfin (遠方)》之銘言：
: 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)] = ?
: 感激不盡！
1. 設答案為w，
w(x+y+z) = ......(請自行整理)
= [x^2/(y+z)]+[y^2/(z+x)]+[z^2/(x+y)]+x+y+z = x+y+z
(x+y+z)不為0，w=1
2. 已知[x/(y+z)]+[y/(z+x)]+[z/(x+y)] = 1
展開之，整理後得x^3+y^3+z^3+xyz=0
又xyz不為0，同除xyz得[x^2/(yz)]+[y^2/(zx)]+[z^2/(xy)]+1=0
所求為-1
其實我會想po是想請問第二小題是否有更elegant的解法，總覺得這樣解稍嫌暴力...
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 61.228.244.40
※ 文章網址: http://www.ptt.cc/bbs/tutor/M.1402332194.A.D15.html