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

1/a+1/c=2 => a+c=2ac (a+c)^2=4a^2c^2=4 ==> a^2+c^2=4-2ac
(a+c)/(a^2+c^2)=2ac/[4-2ac]=ac/(2-ac)
a^2*c^2=1 ==> ac=1 ac=-1
(a+c)/(a^2+c^2)=ac/(2-ac) =1