xyz是正数且满足x+y-5z=0和x-y+z=0求(x^2-y^2)/(z^2-x^2)rtrt

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xyz是正数且满足x+y-5z=0和x-y+z=0求(x^2-y^2)/(z^2-x^2)rtrt
xyz是正数且满足x+y-5z=0和x-y+z=0求(x^2-y^2)/(z^2-x^2)
rtrt

xyz是正数且满足x+y-5z=0和x-y+z=0求(x^2-y^2)/(z^2-x^2)rtrt
两式相加得:2x-4z=0
x=2z代入x+y-5z=0得y=3z
(x^2-y^2)/(z^2-x^2)=(4z²-9z²)/(z²-4z²)=5/3

x+y-5z=0 (1)
x-y+z=0 (2)
(1)+(2): x=2z
(1)变换: x+y=5z
(2)变换: x-y=z
(x^2-y^2)/(z^2-x^2)=(x+y)(x-y)/(z²-x²)=5z×z/(z²-4z²)=5/3

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