Inegalitate in n variabile

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alex2008
Leibniz
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Joined: Sun Oct 19, 2008 3:23 pm
Location: Tulcea

Inegalitate in n variabile

Post by alex2008 »

Fie \( x_1,x_2,...,x_n> 0 \) astfel incat \( \sum_{k=1}^n\frac{1}{1+x_k}=1 \) . Sa se demonstreze ca :

\( x_1x_2...x_n\ge n^{n+1} \)
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
Gauss
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Location: Gaesti (Dambovita)

Post by Marius Mainea »

\( x_k=\frac{\sum_{i\neq k}a_i}{a_k} \) si apoi AM-GM.
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