[b/(1+a^2)]+[a/(1+b2)^2]=[b/(ab+a^2)]+[a/(ab+b2)^2]=[b/(a(b+a))]+[a/(b(a+b))]=(a^2+b^2)/(a+b)=(a+b)^2/(a+b)-2ab/(a+b)=(a+b)-2/(a+b)>=2-2/2=1所以原式的最小值为1,当a=b=1时