已知：4X-3Y-6Z=0,X+2Y-7Z=0,则2X^2+3Y^2+6Z^2 / X^2+5Y^2+7Z^2的值为：A.1 B.2 C.1/2 D.2/3

已知：4X-3Y-6Z=0,X+2Y-7Z=0,则2X^2+3Y^2+6Z^2 / X^2+5Y^2+7Z^2的值为：A.1 B.2 C.1/2 D.2/3
已知：4X-3Y-6Z=0,X+2Y-7Z=0,则2X^2+3Y^2+6Z^2 / X^2+5Y^2+7Z^2的值为：
A.1 B.2 C.1/2 D.2/3

已知：4X-3Y-6Z=0,X+2Y-7Z=0,则2X^2+3Y^2+6Z^2 / X^2+5Y^2+7Z^2的值为：A.1 B.2 C.1/2 D.2/3
X+2Y-7Z=0 则 x=7z-2y
将x=7z-2y代入4X-3Y-6Z=0
则4（7z-2y）-3y-6z=0
化简 y=2z
x=7z-2y=3z
则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=1
A

把Z当作已知数，4X-3Y=6Z, X+2Y=7Z，得出X=3Z，Y=2Z
2X^2+3Y^2+6Z^2 / X^2+5Y^2+7Z^2
=18Z^2+12Z^2+6Z^2/9Z^2+20Z^2+7Z^2
=36Z^2/36Z^2
=1
选A

选A.
4X-3Y-6Z=0, (1)
X+2Y-7Z=0, (2)
(2)*4得:4X+8Y-28Z=0, (3)
(1)-(3)得:-11Y+22Z=0,
所以Y=2Z,
所以X=7Z-2Y=7Z-2*2Z=3Z,
所以(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]
=(18Z^2+12Z^2+6Z^2)/(9Z^2+20Z^2+7Z^2)
=36Z^2/36Z^2
=1.