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Question Number 148364 by mathdanisur last updated on 27/Jul/21

Commented by dumitrel last updated on 27/Jul/21

$$\iff {({ae}^{\frac{x}{2}}+{be}^{\frac{y}{2}})}^2⩾e^{\frac{ax+by}{a+b}}\iff$$$${ae}^{\frac{x}{2}}+{be}^{\frac{y}{2}}⩾e^{\frac{ax+by}{2(a+b)}}$$$$f\left(x\right)=e^{\frac{x}{2}}convexa;\frac{a}{a+b}+\frac{b}{a+b}=1\Rightarrow$$$$\frac{a}{a+b}{e}^{\frac{x}{2}}+\frac{b}{a+b}{e}^{\frac{y}{2}}⩾c^{\frac{a}{a+b}\cdot \frac{x}{2}+\frac{b}{a+b}\cdot \frac{y}{2}}=e^{\frac{ax+by}{2(a+b)}}$$

Commented by mathdanisur last updated on 27/Jul/21

$$ThankyouSer$$

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