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

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

已知3x-4y-z=0 2x+y-8z=0 求(x^2+y^2+z^2)/(xy+yz+2zx)的值快啊!
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
2x+y-8z=0
x=3z,y=2z
(x^2+y^2+z^2)/(xy+yz+2zx)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+6z^2)
=1

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
(x²+y²+z²)/(xy+yz+2zx)
=(9z²+4z²+z²)/(6z²+2z²+6z²)
=(14z²)/(14z²)
=1

把z当作已知数，解二元一次方程得 x=3z，y=2z;
带入所求式子得到
(x^2+y^2+z^2)/(xy+yz+2zx)
=(9z^2+4z^2+z^2)/(6z^2+2z^2+6z^2)
=14/14
=1

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