x(x+y+z)=6 (1)
y(x+y+z)=12 (2)
z(x+y+z)=18 (3)
(2)÷(1)
y/x=2
y=2x
(3)÷(1)
z/x=3
z=3x
所以x(x+y+z)=6则x(x+2x+3x)=6
6x2=6
x=±1
所以
x=1,y=2,z=3
x=-1,y=-2,z=-3