问题 填空题
x
y+z
=
y
z+x
=
z
y+x
=k,则k=______.
答案

x+y+z=0时,y+z=-x,

∴k=

x
-x
=-1,

x+y+z≠0时,k=

x
y+z
=
y
z+x
=
z
y+x
=
x+y+z
2(x+y+z)
=
1
2

综上所述k=

1
2
或-1.

故答案为:

1
2
或-1.

单项选择题
单项选择题