Inegalitate conditionata cu suma variabilelor egala cu trei

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alex2008
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Inegalitate conditionata cu suma variabilelor egala cu trei

Post by alex2008 »

Fie \( a,b,c\ge 0 \) astfel incat \( a+b+c=3 \) . Sa se demonstreze ca :

\( \frac{1}{2ab^2+1}+\frac{1}{2bc^2+1}+\frac{1}{2ca^2+1}\ge 1 \)
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
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Post by Marius Mainea »

Aducand la acelasi numitor inegalitatea este echivalenta cu

\( ab^2+bc^2+ca^2+1\ge 4a^2b^2c^2 \) care este adevarata din AM-GM.
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