(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=?
问题描述:
(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=?
答
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