19.
[tex]\it a)\ \sqrt{(x+2)(x+3)}=\sqrt{12} \Rightarrow (x+2)(x+3)=12=3\cdot4=-4\cdot(-3) \Rightarrow \\ \\ \Rightarrow x+2\in\{-4,\ 3\}|_{-2} \Rightarrow x\in\{-6,\ 1\}[/tex]
[tex]\it b)\ \sqrt{x+2}\cdot\sqrt{x+3}=\sqrt{12}\\ \\ \sqrt{x+2} \Rightarrow x+2\geq0\ (condi\c{\it t}ie\ de\ existen\c{\it t}\breve a)\ \ \ \ \ (*)\\ \\ \sqrt{x+2}\cdot\sqrt{x+3}=\sqrt{12} \Rightarrow (x+2)(x+3)=12=3\cdot4=-4\cdot(-3)\stackrel{(*)}{\Longrightarrow}\\ \\ \Rightarrow x+2=3 \Rightarrow x=1\ \ (solu\c{\it t}ie\ \ unic\breve a)[/tex]
