解:其中(X+1/Y)(Y+1/Z)(Z+1/X)=28/3, 展开即有xyz+1/xyz+(x+y+z)+(1/x+1/y+1/z)=28/3, 三个式子相加有:(x+y+z)+(1/x+1/y+1/z)=22/3; 两式子相减有:xyz+1/xyz=2,XYZ=1;