Question

解方程组{x(x+y+z)=6,y(x+y+z)=12,z(x+y+z)=18

Answer 1

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