已知{4x-3y-6z=0 x+2y-7z=0,并且z≠0 (1)求x:y (2)求x:y:z
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已知{4x-3y-6z=0 x+2y-7z=0,并且z≠0 (1)求x:y (2)求x:y:z
(3)(2x²+3y²+6z²)\(x²+5y²+7z²)
(3)(2x²+3y²+6z²)\(x²+5y²+7z²)
(1)4x-3y-6z=0①
x+2y-7z=0②
①×7-②×6→22x-33y=0
所以x:y=3:2
(2) x=3y/2③ 代入②中
3y/2+2y-7z=0
7y/2=7z
z=y/2④
所以x:y:z=3y/2:y:y/2=3/2:1:1/2=3:2:1
(3) x=3z,y=2z 代入2x²+3y²+6z²)\(x²+5y²+7z²)中
则原式=[2×(3z)²+3×(2z)²+6z²]/[(3z)²+5×(2z)²+7z²]
=36z²/36z²
=1
x+2y-7z=0②
①×7-②×6→22x-33y=0
所以x:y=3:2
(2) x=3y/2③ 代入②中
3y/2+2y-7z=0
7y/2=7z
z=y/2④
所以x:y:z=3y/2:y:y/2=3/2:1:1/2=3:2:1
(3) x=3z,y=2z 代入2x²+3y²+6z²)\(x²+5y²+7z²)中
则原式=[2×(3z)²+3×(2z)²+6z²]/[(3z)²+5×(2z)²+7z²]
=36z²/36z²
=1
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