(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 09:20:24
(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?

(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?
(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?

(x+y-xy)/(x+y+2xy)=(y+z-2yz)/(y+z+3yz)=(z+x-3zx)/(z+x+4zx),且2/x=3/y=1/z,则xyz=?
设2/x=3/y=1/z为k
x=2k,y=3k,z=k
代入得1-k/1+2k=4-6k/4+9k=3-6k/3+8k
算出k得k=-1
x=-2,y=-3,z=-1
xyz=-6

无解~~
令2/x=3/y=1/z=1/t
则:x=2t,y=3t,z=t
代入方程分子分母同消去t得:
(5+6t)/(5+12t)=(4-6t)/(4+9t)=(3-6t)/(3+8t)
无解

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