求解此方程组 x(x+y+z)=6.y(x+y+z)=12.z(x+y+z)=18

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求解此方程组 x(x+y+z)=6.y(x+y+z)=12.z(x+y+z)=18

求解此方程组 x(x+y+z)=6.y(x+y+z)=12.z(x+y+z)=18
求解此方程组 x(x+y+z)=6.y(x+y+z)=12.z(x+y+z)=18

求解此方程组 x(x+y+z)=6.y(x+y+z)=12.z(x+y+z)=18
相加:
(x+y+z)^2=36
x+y+z=±6
(1)x+y+z=6
x=6/6=1
y=12/6=2
z=18/6=3
同理
(2)x+y+z=-6
x=6/-6=-1
y=12/-6=-2
z=18/-6=-3
两解.
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X=1,Y=2,Z=3