已知(X+Y)/Z=(X+Z)/Y=(Y+Z)/X,且XYZ≠0,则(X+Y)(Y+Z)(Z+x)/XYZ的值为

[x+y]/z=[y+z]/x=[z+x]/y
设[x+y]/z=[y+z]/x=[z+x]/y=k

x+y=kz,y+z=kx,z+x=ky
三式相加得:2(x+y+z)=k(x+y+z)
(1)x+y+z=0:
(x+y)(y+z)/(z+x)/xyz=(-z)(-x)(-y)/xyz=-1

(2)x+y+z=/=0,则k=2.

(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8

:2(x+y+z)=k(x+y+z)
咋算等于 x+y+z=0的啊

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