Question

Demonstrati ca x^2+3x+3>0 , pentru orice x apartine lui R

Answer 1

$x^2+3x+3\ \textgreater \ 0 \\ \\ Consideram functia: f(x) = x^2+3x+3 \\ \\\\ \Delta = b^2-4ac = 3^2-4\cdot1\cdot 3 = 9-12 = -3 \ \textless \ 0 \\ \\ Avem: \left\{ \begin{array}{c} a\ \textgreater \ 0 \\ \Delta \ \textless \ 0 \end{array} \right| \Rightarrow f(x) \ \textgreater \ 0,\quad \forall x\in \mathbb_{R}$