若 \(a,b\ge 0< pq=p+q,\)则 \(ab=\underset{t>0}{\inf}((at)^p/p+(b/t)^q/q)\)

elim

题：试证若\(\,a,b\ge 0< pq=p+q,\,\)则\(\,\displaystyle ab=\inf_{t>0}\left(\frac{t^p}{p}a^p+\frac{t^{-q}}{q}b^q\right)\).