Inegalitate in triunghi

[Mateescu Constantin]

\( \left\|\ \begin{array}{cc}
<<<\ \triangle ABC\ >>> \\\\\\\\
a+b+c=4\end{array}\ \right\|\ \Longrightarrow\ abc+a^2+b^2+c^2\ <\ 8 \)

[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.