已知4x-3y-6z=0,x+2y-7z=0,则2xy+3yz-6zx / x^2+5y^2+7z^2=_______

已知4x-3y-6z=0,x+2y-7z=0,则2xy+3yz-6zx / x^2+5y^2+7z^2=_______
已知4x-3y-6z=0,x+2y-7z=0,则2xy+3yz-6zx / x^2+5y^2+7z^2=_______

已知4x-3y-6z=0,x+2y-7z=0,则2xy+3yz-6zx / x^2+5y^2+7z^2=_______
由4x-3y-6z=0,x+2y-7z=0 解得x=3z y=2z代入2xy+3yz-6zx / x^2+5y^2+7z^2
得原式=0

4x-3y-6z=0.......(1)
x+2y-7z=0........(2)
(2)*4-(1),得
11y-22z=0
y=2z
(1)*2+(2)*3,得
11x-33z=0
x=3z
把x=3z，y=2z代入所求式得2
(xy+3yz-6zx) / (x^2+5y^2+7z^2)
=(6z²+6z²-18z²)/(9z²+20z²+7z²)
=-6z²/36z²
=-6/36
=-1/6