Question

Cea mai mica valoare a nr
$\sqrt{a^2-6a+13}$

unde a apartine R

Answer 1

   
[tex]\displaystyle\\ \bf\\ \text{Expresia are un minim deoarece coeficientul lui }a^2 \text{ este pozitiv.}\\\\ Minimul ~expresiei ~~ \sqrt{a^2-6a+13} ~~~este: \\\\ minim = \sqrt{ \frac{-\Delta}{4a}} = \sqrt{ \frac{-(b^2-4ac)}{4a}} = \sqrt{ \frac{-((-6)^2-4\cdot 1 \cdot 13)}{4\cdot 1}} =\\\\\\ = \sqrt{ \frac{-(36-52)}{4}} =\sqrt{ \frac{-(-16)}{4}} =\sqrt{ \frac{16}{4}} =\sqrt{4} = \boxed{\bf 2}[/tex]