Subiectul 3 ONM 2008

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Bogdan Cebere
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Subiectul 3 ONM 2008

Post by Bogdan Cebere »

Fie \( a,b \in [0,1] \). Demonstrati inegalitatea: \( \frac{1}{1+a+b} \leq 1- \frac{a+b}{2}+\frac{ab}{3} \).
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Claudiu Mindrila
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Post by Claudiu Mindrila »

Inegalitatea este echivalenta cu \( (1-a)(1-b)(a+b)+ ab(1-a+1-b) \ge 0 \), inegalitate adevarata tinand cont ca \( a,b\in [0,1] \).
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
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