已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值

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已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值
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已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值
已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值

已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值
由3x-4y-z=0得z=3x-4y ③
由2x+y-8z=0得y=8z-2x ④
④代入③得 x=3z ⑤
y=2z
将x,y代入
(x^2+y^2+z^2)/(xy+yz+2zx)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+6z^2)
=(14z^2)/(14z^2)
=1

3x-4y-z=0得z=3x-4y ③
2x+y-8z=0得y=8z-2x ④
④代入③得 x=3z
y=2z
将x,y代入
(x^2+y^2+z^2)/(xy+yz+xz)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+2z)
=14/11