已知x+y/xy=1,y+z/yz=2,x+z/xz=3求x+y+z的值

Question

已知x+y/xy=1,y+z/yz=2,x+z/xz=3求x+y+z的值

Answer 1

1=xy/(x+y)两边倒数1/x+1/y=1
同理 1/y+1/z=1/2
1/z+1/x=1/3
联合三个方程得1/x=5/12 1/y=7/12 1/z=-1/12
即x=12/5 y=12/7 z=-12
x+y+z=-276/35