已知a,b,c满足方程组:a-2b-c=0,2a+b+c=0,且abc不等于0,求a:b:c
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已知a,b,c满足方程组:a-2b-c=0,2a+b+c=0,且abc不等于0,求a:b:c
![已知a,b,c满足方程组:a-2b-c=0,2a+b+c=0,且abc不等于0,求a:b:c](/uploads/image/z/7450554-66-4.jpg?t=%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%E6%BB%A1%E8%B6%B3%E6%96%B9%E7%A8%8B%E7%BB%84%EF%BC%9Aa-2b-c%3D0%2C2a%2Bb%2Bc%3D0%2C%E4%B8%94abc%E4%B8%8D%E7%AD%89%E4%BA%8E0%2C%E6%B1%82a%3Ab%3Ac)
a-2b-c=0(1)
2a+b+c=0(2)
(1)+(2)得:3a-b=0,3a=b.a:b=1:3
(2)*2得:4a+2b+2c=0(3)
(1)+(3)得:5a+c==,5a=-c,a:c=1:(-5)
所以a:b:c=1:3:(-5)
2a+b+c=0(2)
(1)+(2)得:3a-b=0,3a=b.a:b=1:3
(2)*2得:4a+2b+2c=0(3)
(1)+(3)得:5a+c==,5a=-c,a:c=1:(-5)
所以a:b:c=1:3:(-5)
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