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Inegalitate in triunghi

Posted: Thu Jul 02, 2009 12:58 pm
by Mateescu Constantin
\( \left\|\ \begin{array}{cc}
<<<\ \triangle ABC\ >>> \\\\\\\\
a+b+c=4\end{array}\ \right\|\ \Longrightarrow\ abc+a^2+b^2+c^2\ <\ 8 \)

Posted: Fri Jul 03, 2009 3:25 pm
by Marius Mainea
Deoarece \( (a-2)(b-2)(c-2)<0 \) obtinem \( abc+8<2(ab+bc+ca) \) (*)

Adunand in ambii termeni ai (*) \( a^2+b^2+c^2 \) obtinem concluzia.