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
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![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](/uploads/image/z/584567-71-7.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A4X-3Y-6Z%3D0%2CX%2B2Y-7Z%3D0%2C%E5%88%992X%5E2%2B3Y%5E2%2B6Z%5E2+%2F+X%5E2%2B5Y%5E2%2B7Z%5E2%E7%9A%84%E5%80%BC%E4%B8%BA%EF%BC%9AA.1+B.2+C.1%2F2+D.2%2F3)
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.