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Question Number 151212 by mathdanisur last updated on 19/Aug/21

$$\mathrm{if}{\mathrm{a}}_1,{\mathrm{a}}_2,...{\mathrm{a}}_{\mathbf{n}}>1\mathrm{then}:$$$$\sqrt{\frac{({\mathrm{a}}_1-1)({\mathrm{a}}_2-1)...({\mathrm{a}}_{\mathbf{n}}-1)}{({\mathrm{a}}_1+1)({\mathrm{a}}_2+1)...({\mathrm{a}}_{\mathbf{n}}+1)}}⩽\frac{{\mathrm{a}}_1{\mathrm{a}}_2...{\mathrm{a}}_{\mathbf{n}}}{2^{\mathbf{n}}}$$

Answered by dumitrel last updated on 19/Aug/21

$$x⩾1\Rightarrow \sqrt{\frac{x-1}{x+1}}<\frac{x}{2}\iff x^3+{(x-2)}^2>0$$$$$$

Commented by mathdanisur last updated on 19/Aug/21

$$\mathrm{Cool}\mathbf{S}\mathrm{er},\mathrm{thank}\mathrm{you}$$

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