Question

若

x

y+z

=

y

z+x

=

z

y+x

=k，则k=______．

Answer 1

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．