Iasi 2006

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alex2008
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Iasi 2006

Post by alex2008 »

Fie \( x,y,z\in \mathbb{R} \) cu \( xyz=1 \). Sa se arate ca:

\( \sum_{cyc}\frac{1+xy}{1+z}\ge 3 \).

Etapa locala Iasi 2006
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Claudiu Mindrila
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Post by Claudiu Mindrila »

Avem: \( \sum\frac{1+xy}{1+z}=\sum\frac{1+xy}{z\left(1+xy\right)}=\sum\frac{1}{z}=\sum xy\ge3\sqrt[3]{\left(xyz\right)^{2}}=3 \).
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
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