设：(x+y-z)/z=(y+z-x)/x=(z+x-y)/y =k
{x+y-z=kz (1)
{y+z-x=kx (2)
{z+x-y=ky (3)
(1)+(2)+(3)得:
(x+y+z)=k(x+y+z)
(x+y+z)(k-1)=0
k=1或x+y+z=0
当k=1时
{x+y-z=z
{y+z-x=x
{z+x-y=y
解得
x=y=z (x+y)(y+z)(z+x)/xyz=8
当x+y+z=0时
(x+y)(y+z)(z+x)/xyz=(-z)(-x)(-y)/xyz=-1
(x+y-z)/z=(y+z-x)/x=(z+x-y)/y 求(x+y)(y+z)(z+x)/xyz
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