x-y+z=0,x+y-5z=o,xyz≠0,求x^2+y^2+z^2/2x^2+y^2-z^2的值

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x-y+z=0,x+y-5z=o,xyz≠0,求x^2+y^2+z^2/2x^2+y^2-z^2的值

x-y+z=0,x+y-5z=o,xyz≠0,求x^2+y^2+z^2/2x^2+y^2-z^2的值
x-y+z=0,x+y-5z=o,xyz≠0,求x^2+y^2+z^2/2x^2+y^2-z^2的值

x-y+z=0,x+y-5z=o,xyz≠0,求x^2+y^2+z^2/2x^2+y^2-z^2的值
x-y+z=0````````````````````1
x+y-5z=o``````````````````2
联立1、2解得:
y=3z, x=2z
(x^2+y^2+z^2)/(2x^2+y^2-z^2)
=[(2z)^2+(3z)^2+z^2]/[2(2z)^2+(3z)^2-z^2]
=14z^2/16z^2
=7/8

∵x-y+z=0 x+y-5z=0 ∴x=2z y=3z
∴(x²+y²+z²)/(2x²+y²-z²)=(4z²+9z²+z²)/(8z²+9z²-z²)=14z²/15z²=14/15