已知a比b等于b比c等于c比d等于d比a,求a加b加c加d比a加b加c减d

Question

已知a比b等于b比c等于c比d等于d比a,求a加b加c加d比a加b加c减d

Answer 1

设a/b=b/c=c/d=d/a=k,则
a/b*b/c*c/d*d/a=k^4=1,
∴k^2=土1,
∴k=土1,土i,
d=ak,c=ak^2,b=ak^3,
∴(a+b+c+d)/(a+b+c-d)=(1+k^3+k^2+k)/(1+k^3+k^2-k)
=2,或0,或0,或0.