Question

设a,b∈(0,+无穷),且满足ab=1,探究使不等式a/(a^2+1)+b/(b^2+1)

Answer 1

(a+b)^2>=4ab=4

所以a+b>=2

a/(a^2+1)+b/(b^2+1)

=a/(a^2+ab)+b/(b^2+ab)

=2/(a+b)

=1