已知x+y:z=y+z:x=z+x:y,求（x+y)(y+z)(z+x):xyz的值已知x^2-3xy-4y^2=0且xy不等于0,求x:y的值.

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已知x+y:z=y+z:x=z+x:y,求（x+y)(y+z)(z+x):xyz的值已知x^2-3xy-4y^2=0且xy不等于0,求x:y的值.
已知x+y:z=y+z:x=z+x:y,求（x+y)(y+z)(z+x):xyz的值
已知x^2-3xy-4y^2=0且xy不等于0,求x:y的值.

已知x+y:z=y+z:x=z+x:y,求（x+y)(y+z)(z+x):xyz的值已知x^2-3xy-4y^2=0且xy不等于0,求x:y的值.
1、
令k=(x+y)/z=(y+z)/x=(z+x)/y
x+y=kz
y+z=kx
z+x=ky
相加
2(x+y+z)=k(x+y+z)
(k-2)(x+y+z)=0
k=2或x+y+z=0
x+y+z=0
则x+y=-z
k=(x+y)/z=-1
所以k=2,k=-1
所以原式=[(x+y)/z]*[(y+z)/x]*[(z+x)/y]=k³=8或-1
2、
(x-4y)(x+y)=0
x-4y=0,x+y=0
x=4y,x=-y
所以x:y=4或-1

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