已知a/b=b/c=c/d=d/a=k,求(a+b+c+d)/(a+b+c-d)的值是多少?
问题描述：
已知a/b=b/c=c/d=d/a=k,求(a+b+c+d)/(a+b+c-d)的值是多少?
答
d = ak
c = dk = ak^2
b = ck = ak^3
a + b + c + d = a( 1 + k + k^2 + k^3 )
a + b + c - d = a( 1 + k + k^2 - k^3 )
(a+b+c+d)/(a+b+c-d) = ( 1 + k + k^2 + k^3 )/( 1 + k + k^2 - k^3 )