实数1/a,a,1/c成等差数列,实数a^2,1,c^2成等比数列,则(a+c)/(a^2+c^2)=?

因为a^2 1 c^2成等比数列,所以1^2=a^2*c^2ac=±1因为1/a a 1/c成等差数列,所以2a=1/a+1/c=(a+c)/ac当ac=1时,2a=a+c a=c(a+c)/(a^2+c^2)=2a/2a^2=1/a=±1当ac=-1时,2a=-a-c 3a=-c(a+c)/(a^2+c^2)=(a-3a)/(a^2+9a^2)=-...