解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18
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解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18解方程组{x(x+y+z)=6,y(x+y+
解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18
解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18
解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18
x(x+y+z)=6 (1)
y(x+y+z)=12 (2)
z(x+y+z)=18 (3)
(1)/(2)
x/y=1/2
y=2x
(1)/(3)
x/z=1/3
z=3x
x(x+2x+3x)=6
6x^2=6
x=1 y=2 z=3
x=-1 y=-2 z=-3
x(x+y+z)=6,①
y(x+y+z)=12,②
z(x+y+z)=18,③
②/①，可得，y=2x
③/②，可得，z=3x
将y=2x，z=3x代入①，可得
6x^2=6，x^2=1
x=1,y=2,z=3
x= -1, y= -2, z= -3
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