O inegalitate elementara

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Claudiu Mindrila
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O inegalitate elementara

Post by Claudiu Mindrila »

Demonstrati ca pentru orice numere \( a,b,c \in (0, \infty) \), are loc inegalitatea \( (a+b)(ab+1)+(b+c)(bc+1)+(c+a)(ca+1) \geq 4(ab+bc+ca) \).

Zdravko Starc, Revista Minus 1/2008
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 »

\( \sum {(a+b)(ab+1)}\geq\sum {2\sqrt{ab}2\sqrt{ab}}=4\sum {ab} \)
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