已知4x-3y-6z=0,x+2y-7z=0.求2x^2+3y^2+6z^2/x^2+5y^2+7z^2的值

已知4x-3y-6z=0,x+2y-7z=0.求2x^2+3y^2+6z^2/x^2+5y^2+7z^2的值
已知4x-3y-6z=0,x+2y-7z=0.求2x^2+3y^2+6z^2/x^2+5y^2+7z^2的值

已知4x-3y-6z=0,x+2y-7z=0.求2x^2+3y^2+6z^2/x^2+5y^2+7z^2的值
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
2x^2+3y^2+6z^2/x^2+5y^2+7z^2
=[2*(3z)^2+3*(2z)^2+6z^2]/[(3z)^2+5*(2z)^2+7z^2]
=36z^2/(36z^2)
=1