设a,b,c是三个不相等的正数,且满足(a—c)/b=c/(a+b)=b/a,则有A.3b=2c B.3a=2b C.2b=c D.2a=b帮我看看啊~选什么?怎么算出来的?
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![设a,b,c是三个不相等的正数,且满足(a—c)/b=c/(a+b)=b/a,则有A.3b=2c B.3a=2b C.2b=c D.2a=b帮我看看啊~选什么?怎么算出来的?](/uploads/image/z/5084651-11-1.jpg?t=%E8%AE%BEa%2Cb%2Cc%E6%98%AF%E4%B8%89%E4%B8%AA%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84%E6%AD%A3%E6%95%B0%2C%E4%B8%94%E6%BB%A1%E8%B6%B3%EF%BC%88a%E2%80%94c%EF%BC%89%2Fb%3Dc%2F%EF%BC%88a%2Bb%EF%BC%89%3Db%2Fa%2C%E5%88%99%E6%9C%89A.3b%3D2c+B.3a%3D2b+C.2b%3Dc+D.2a%3Db%E5%B8%AE%E6%88%91%E7%9C%8B%E7%9C%8B%E5%95%8A%7E%E9%80%89%E4%BB%80%E4%B9%88%3F%E6%80%8E%E4%B9%88%E7%AE%97%E5%87%BA%E6%9D%A5%E7%9A%84%3F)
设a,b,c是三个不相等的正数,且满足(a—c)/b=c/(a+b)=b/a,则有A.3b=2c B.3a=2b C.2b=c D.2a=b帮我看看啊~选什么?怎么算出来的?
设a,b,c是三个不相等的正数,且满足(a—c)/b=c/(a+b)=b/a,则有A.3b=2c B.3a=2b C.2b=c D.2a=b
帮我看看啊~选什么?怎么算出来的?
设a,b,c是三个不相等的正数,且满足(a—c)/b=c/(a+b)=b/a,则有A.3b=2c B.3a=2b C.2b=c D.2a=b帮我看看啊~选什么?怎么算出来的?
(a-c)/b=b/a,所以b^2=a^2-ac
c/(a+b)=b/a,所以ac=ab+b^2
两式替换ac:
b^2=a^2-ab-b^2
a^2-ab-2b^2=0
(a-2b)(a+b)=0
a=2b或a=-b
把a=2b代入(a-c)/b=b/a
(2b-c)/b=b/2b
2c=3b
把a=-b代入(a-c)/b=b/a
(-b-c)/b=b/(-b)
c=0
所以应选A