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Concursul GM "Nicolae Teodorescu" 2009, problema 3

Posted: Tue Aug 18, 2009 7:47 pm
by Laurentiu Tucaa
Consideram numerele \( a,b,c,d>1 \) astfel incat \( a+b+c+d=8 \). Sa se demonstreze inegalitatea: \( a^{a^2}b^{b^2}c^{c^2}d^{d^2} \ge 65536 \).

Viorel Tudoran, Ucu Crisan

Posted: Tue Aug 18, 2009 7:58 pm
by Marius Mainea
Functia \( f : (1,\infty)\rightarrow\mathbb{R} \) \( f(x)=x^2\ln x \) este convexa si aplicam Jensen.