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
问题描述：
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
答
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
答
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