4x-3y-6z=0---(1)
x+2y-7z=0---(2)
整理(1)(2)
4x-3y=6z---(3)
x+2y=7z---(4)
(3)*2+(4)*3
11x=33z
x=3z
(4)*4-(3)
11y=22z
y=2z
2x^2+3y^2+6z^2=2(3z)^2+3(2z)^2+6z^2=36z^2
x^2+5y^2+7z^2=(3z)^2+5(2z)^2+7z^2=36z^2
(2x^2+3y^2+6z^2)/(x^2+5y^2+7z^2=1