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

if a_{1}, a_{2}, \dots a_{n} > 1 then :

\sqrt{\frac{(a_{1} - 1) (a_{2} - 1) \dots (a_{n} - 1)}{(a_{1} + 1) (a_{2} + 1) \dots (a_{n} + 1)}} ⩽ \frac{a_{1} a_{2} \dots a_{n}}{2^{n}}

Answered by dumitrel last updated on 19/Aug/21

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

Commented by mathdanisur last updated on 19/Aug/21

Cool S er, thank you