已知abc是三个互不相等的正数,若(a-c)/b=c/(a+b)=b/a,求a:b:c=

Question

已知a b c是三个互不相等的正数,若(a-c)/b=c/(a+b)=b/a,求a:b:c=

Answer 1

设(a-c)/b=c/(a+b)=b/a=k则a-c=bk.(1)c=(a+b)k.(2)b=ak.(3)(2)(3)代入(1)得a-(a+b)k=bka-ak=2ak²2k²+k-1=0(k+1)(2k-1)=0又a b c是三个互不相等的正数,k>0解得k=1/2b/a=k=1/2又c=(a+b)k即2c=3bb/c=2/3综上a...