Inegalitate draguta

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Claudiu Mindrila
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Inegalitate draguta

Post by Claudiu Mindrila »

Fie \( a,b,c,>0 \) cu \( abc=8 \). Sa se arate ca: \( \frac{a-2}{a+1}+\frac{b-2}{b+1}+\frac{c-2}{c+1}\leq 0 \)
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
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Marius Mainea
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Post by Marius Mainea »

Inegalitatea se scrie \( \sum{\frac{a+1-3}{a+1}}\le 0 \) sau

\( \sum{\frac{1}{a+1}}\ge 1 \) sau

\( \sum{\frac{y}{2x+y}}\ge 1 \) unde am notat \( a=\frac{2x}{y} \) si analoagele.

Mai departe se aplica inegalitatea CBS.
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