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Inegalitate conditionata
Posted: Fri May 08, 2009 12:10 pm
by BogdanCNFB
Fie \( a,b,c \) trei numere reale strict pozitive cu media aritmetica \( 4\sqrt{2}-1 \).
Demonstrati ca \( \sum\frac{1}{a^2+b}\ge 1 \).
Posted: Sun May 10, 2009 10:35 am
by alex2008
Incearca
\( a=b=c=2\sqrt{2}-1 \) .
Posted: Sun May 10, 2009 12:53 pm
by BogdanCNFB
Da, cred ca este gresita. Am luat-o dintr-o culegere mai veche.
Re: Inegalitate conditionata
Posted: Sun May 10, 2009 4:30 pm
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.