已知4x-3y-6z=0x+2y-7z=0求：(2x^2+8y^2+5z^2)/(x^2+4y^2+7z^2)

Question

已知 4x-3y-6z=0
x+2y-7z=0
求：(2x^2+8y^2+5z^2)/(x^2+4y^2+7z^2)

Answer 1

由4x-3y-6z=0,(1式)
x+2y-7z=0(2式)
(2式)*4得:
4x+8y-28z=0(3式)
(3式)-(1式)得:
4x+8y-28z-(4x-3y-6z)=0
4x+8y-28z-4x+3y+6z=0
11y-22z=0
y=2z(4式)
将y=2z代入(2式)中得
x+2y-7z=x+2*2z-7z=x-3z=0
x=3z(5式)
将(4式)、(5式)代入
(2x^2+8y^2+5z^2)/(x^2+4y^2+7z^2),得
(2x^2+8y^2+5z^2)/(x^2+4y^2+7z^2)=55z^2/32z^2=55/32