若实数x,y,z满足方程组:xyx+2y=1…(1)yzy+2z=2…(2)zxz+2x=3…(3),则有(  ) A.x+2y+3z=0 B.7x+5y+2z=0 C.9x+6y+3z=0 D.10x+7y+z=0

问题描述:

若实数x,y,z满足方程组:

xy
x+2y
=1…(1)
yz
y+2z
=2…(2)
zx
z+2x
=3…(3)
,则有(  )
A. x+2y+3z=0
B. 7x+5y+2z=0
C. 9x+6y+3z=0
D. 10x+7y+z=0

由(1)、(3)得y=

x
x−2
z=
6x
x−3

故x≠0,代入(2)解得x=
27
10

所以y=
27
7
,z=-54.
检验知此组解满足原方程组.
∴10x+7y+z=0.
故选D.