[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]
