2y+z=kx(1)
2x+y=kz(2)
2z+x=ky(3)
(1)+(2)+(3)得
3(x+y+z)=k(x+y+z)
3(x+y+z)-k(x+y+z)=0
3(x+y+z)(3-k)=0
因为x+y+z不等于0
所以3-k=0
即k=3
若x+y+z=0,则k取R
2y+z=kx(1)
2x+y=kz(2)
2z+x=ky(3)
(1)+(2)+(3)得
3(x+y+z)=k(x+y+z)
3(x+y+z)-k(x+y+z)=0
3(x+y+z)(3-k)=0
因为x+y+z不等于0
所以3-k=0
即k=3
若x+y+z=0,则k取R