已知4x-3y-6z=0,x+2y-7z=0,求(2x²+3y²+6z²)/(x²
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已知4x-3y-6z=0,x+2y-7z=0,求(2x²+3y²+6z²)/(x²+5y²+7z²)的值.
![已知4x-3y-6z=0,x+2y-7z=0,求(2x²+3y²+6z²)/(x²](/uploads/image/z/16068613-13-3.jpg?t=%E5%B7%B2%E7%9F%A54x-3y-6z%3D0%2Cx%2B2y-7z%3D0%2C%E6%B1%82%EF%BC%882x%26%23178%3B%2B3y%26%23178%3B%2B6z%26%23178%3B%EF%BC%89%2F%EF%BC%88x%26%23178)
4x-3y-6z=0.①
x+2y-7z=0.②
②*4-①得
8y+3y-28z+6z=0
y=2z
①*2+②*3,得
8x+3x-12z-21z=0
11x-33z=0
x=3z
把x=3z,y=2z代入 所求式得
(2x²+3y²+6z²)/(x²+5y²+7z²)
=[2*(3z)²+3*(2z)²+6z²]/[(3z)²+5*(2z)²+7z²]
=(18z²+12z²+6z²]/(9z²+20z²+7z²]
=36z²/(36z²)
=1
x+2y-7z=0.②
②*4-①得
8y+3y-28z+6z=0
y=2z
①*2+②*3,得
8x+3x-12z-21z=0
11x-33z=0
x=3z
把x=3z,y=2z代入 所求式得
(2x²+3y²+6z²)/(x²+5y²+7z²)
=[2*(3z)²+3*(2z)²+6z²]/[(3z)²+5*(2z)²+7z²]
=(18z²+12z²+6z²]/(9z²+20z²+7z²]
=36z²/(36z²)
=1
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