已知2006(x-y)+2007(y-z)+2008(z-x)=0,2006^2(x-y)+2007^2(y-z)+2008^2(z-x)=2008求z-x
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已知2006(x-y)+2007(y-z)+2008(z-x)=0,2006^2(x-y)+2007^2(y-z)+2008^2(z-x)=2008求z-x
已知2006(x-y)+2007(y-z)+2008(z-x)=0,2006^2(x-y)+2007^2(y-z)+2008^2(z-x)=2008
求z-x
已知2006(x-y)+2007(y-z)+2008(z-x)=0,2006^2(x-y)+2007^2(y-z)+2008^2(z-x)=2008求z-x
(x+y-z)/z=(y+z-x)/x=(z+x-y)/y
[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y
设[x+y]/z=[y+z]/x=[z+x]/y=k
k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z]
k=2
(x+y)(y+z)(z+x)/xyz
=(x+y)/z*(y+z)/x*(z+x)/y=2*2*2=8
x
由题意,得(x+y-z)/z=(y+z-x)/x=(z+x-y)/y
得[x+y]/z-1=[y+z]/x-1=[z+x]/y-1
[x+y]/z=[y+z]/x=[z+x]/y (1)
设 S=(1)
得 S=2
答案 2*2*2=8
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