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Question Number 97637 by Ar Brandon last updated on 09/Jun/20

$$\mathrm{Given}\mathrm{p},\mathrm{q}\in {\mathbb{R}}_{+}^{\ast }-\{-1\}/\frac{1}{\mathrm{p}}+\frac{1}{\mathrm{q}}=1\mathrm{show}\mathrm{that};$$$$\mathrm{\forall }\mathrm{a},\mathrm{b}\in \mathbb{R}\mathrm{ab}⩽\frac{{\mathrm{a}}^{\mathrm{p}}}{\mathrm{p}}+\frac{{\mathrm{b}}^{\mathrm{q}}}{\mathrm{q}}$$

Commented by arcana last updated on 09/Jun/20

$$\mathrm{its}\mathrm{the}{\mathrm{Young}}^{\prime }\mathrm{s}\mathrm{inequality}.\mathrm{You}\mathrm{can}$$$$\mathrm{find}\mathrm{it}\mathrm{in}\mathrm{various}\mathrm{web}\mathrm{pages}$$

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