已知3x-4y-z=0,2x+y-8z=0 求(x²+y²+z²)/(xy+yz+zx)

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已知3x-4y-z=0,2x+y-8z=0 求(x²+y²+z²)/(xy+yz+zx)
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已知3x-4y-z=0,2x+y-8z=0 求(x²+y²+z²)/(xy+yz+zx)
已知3x-4y-z=0,2x+y-8z=0 求(x²+y²+z²)/(xy+yz+zx)

已知3x-4y-z=0,2x+y-8z=0 求(x²+y²+z²)/(xy+yz+zx)
3x-4y-z=0,(1)
2x+y-8z=0(2)
2式*4+1式
可以得到X=3Z
代入2式,
可以得到Y=2Z
所求比值为:9+4+1/6+2+3=14/11

3x-4y-z=0  (1)
2x+y-8z=0  (2)
(2)*4得
8x+4y-32z=0 (3)
(3)+(1)得
11x-33z=0
x=3Z
代入(1)得y=2z
将x=3Z,y=2z,z=z代入得
(x²+y²+z²)/(xy+yz+zx)
=14/11