若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=

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若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=若有xyz≠0,2y+2z/x=2x+2y/z=2z

若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=
若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=

若有xyz≠0,2y+2z/x=2x+2y/z=2z+2x/y=k,则K=
将已知变形:2y+2z=kx,2x+2y=kz,2z+2x=ky,三式相加得:4(x+y+z)=k(x+y+z)
即(4-k)(x+y+z)=0,所以:
1) x+y+z≠0时,
2) x+y+z=0时,y+z=-x,代入第一个式子:-2x=kx,因为x≠0,所以:k=-2
综上可知:k=4或-2