Question

已知1=xy/x+y，2=yz/y+z，3=xz/x+z，求x，y，z的值？

Answer 1

1-----1=xy/(x+y)--->x+y-xy=0---->x=y/(y-1)代入3式
2-----2=yz/(y+z)--->2y+2z-yz=0
3-----3=xz/(x+z)--->3x+3z-xz=0--->3y/(y-1)+3z-yz/(y-1)=0--->z=3y/(3-2y)代入2式得
4-----2y+6y/(3-2y)-3y^2/(3-2y)=0化简得y=12/7,x=(12/7)/(12/7-1)=12/5,
z=3*(12/7)/(3-2*12/7)=-12

Answer 2

xy/x+y=1--->(x+y)/xy=1--->1/x+1/y=1 1
yz/y+z=2--->(y+z)/yz=1/2-->1/y+1/z=1/2 2
zx/z+x=3--->(z+x)/zx=1/3-->1/z+1/x=1/3 3
1/x+1/y+1/z=11/12 4
4-2 1/x=5/12
4-3 1/y=7/12
4-1 1/z=-1/12
x=12/5.y=12/7,z=-12
x+y+z=-276/35