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

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

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