∵a+1/b=b+1/c=c+1/d=d+1/a=x∴a+1/b=x、b+1/c=x、c+1/d=x、d+1/a=xa+1=bx、b+1=cx、c+1=dx、d+1=ax四式相加得a+b+c+d+4=(a+b+c+d)x若a+b+c+d=0，原方程无解若a+b+c+d≠0x=1+4/(a+b+c+d)
