2)
[tex]x_1\ \textless \ 0\ \ si\ \ x_2\ \textgreater \ 0 \Rightarrow x_1\cdot x_2 \ \textless \ 0\ \ \ (1)[/tex]
Aplicam relatiile lui Viete ecuatiei date :
[tex]x_1\cdot x_2 = m\ \ \ (2)[/tex]
Din (1), (2) ⇒ m < 0 ⇒ [tex]m\in (- \infty,\ 0)[/tex]
3)
[tex]C^1_n = 36-A^2_n \Rightarrow n = 36-\dfrac{n!}{(n-2)!} \Rightarrow n= 36-\dfrac{(n-2)!\cdot(n-1)n}{(n-2)!}\\\;\\
\Rightarrow n = 36 -(n-1)n \Rightarrow n = 36- n^2+n \Rightarrow 0 = 36- n^2 \Rightarrow n^2 = 36 [/tex]
⇒n = 6
5)
[tex]\mathcal{A}=\dfrac{AC\cdot BC\cdot sin C}{2}=\dfrac{4\cdot \sqrt3\cdot \sin 60^0}{2} = 2\sqrt3\cdot\dfrac{\sqrt3}{2}=3[/tex]
