Question

若a/b=b/c=c/d=d/a,求(a-b+c-d)/(a+b-c+d)的值.

Answer 1

假设a/b=b/c=c/d=d/a=k

则a=bk,b=ck,c=dk,d=ak

a=bk=(ck)*k=ck^2=dk^3=ak^4

k^4=1

k=1或者k=-1

当k=1时

a=b=c=d

则(a-b+c-d)/(a+b-c+d)=0

当k=-1时

a=-b=c=-d=a

(a-b+c-d)/(a+b-c+d)=(a+a+a+a)/(a-a-a-a)=-2