已知3x-4y=0,2x+y-8z=o,求x2+y2+z2/xy+yz+2zx的值写错了，是3x-4y-z

1721/217

3x-4y-z=0 (1) 2x+y-8z=0 (2)
(1) +(2)*4
11x=33z
x=3z y=2z 代入
x^2+y^2+z^2/2xy+zx-2yz
=(3z)^2+(2z)^2+z^2/2*3z*2z+3z*z-2*2z*z
=14z^2/11z^2
=14/11

3x-4y=0 y=3x/4
2x+y-8z=0 z=11x/32
代入 x2+y2+z2/xy+yz+2zx
即可以把x都消掉
答案是1721/1384=1.24349711

3x-4y=0
x=4y/3
2x+y-8z=o,
z=11y/24
把x2+y2+z2/xy+yz+2zx中
x，z都换成y就可以

3x-4y-z=0,2x+y-8z=0
11x-33z=0
x=3z
y=2z
x2+y2+z2/xy+yz+2zx这是个齐次式,分子分母都除以z^2
x2+y2+z2/xy+yz+2zx
=(9+4+1)/(6+2+6)
=1.