Inegalitate conditionata

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BogdanCNFB
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Inegalitate conditionata

Post by BogdanCNFB »

Fie \( a,b,c \) trei numere reale strict pozitive cu media aritmetica \( 4\sqrt{2}-1 \).
Demonstrati ca \( \sum\frac{1}{a^2+b}\ge 1 \).
Last edited by BogdanCNFB on Sun May 10, 2009 12:48 pm, edited 1 time in total.
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alex2008
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Post by alex2008 »

Incearca \( a=b=c=2\sqrt{2}-1 \) . :?
. A snake that slithers on the ground can only dream of flying through the air.
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BogdanCNFB
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Post by BogdanCNFB »

Da, cred ca este gresita. Am luat-o dintr-o culegere mai veche.
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alex2008
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Re: Inegalitate conditionata

Post by alex2008 »

BogdanCNFB wrote:Fie \( a,b,c \) trei numere reale strict pozitive cu media aritmetica \( 4\sqrt{2}-1 \). Demonstrati ca \( \sum\frac{1}{a^2+b}\ge 1 \).
La fel daca \( a=b=c=4\sqrt{2}-1 \), inegalitatea e mai slaba.
. A snake that slithers on the ground can only dream of flying through the air.
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