Question

Buna, am nevoie de aceste ecuatii irationale. Dau test in aceasta dupa amiaza si as vrea sa vad cum arata niste exemple rezolvate (am nevoie macar de 18,19,20). Multumesc !

Answer 1

19.

$\it a)\ \sqrt{(x+2)(x+3)}=\sqrt{12} \Rightarrow (x+2)(x+3)=12=3\cdot4=-4\cdot(-3) \Rightarrow \\ \\ \Rightarrow x+2\in\{-4,\ 3\}|_{-2} \Rightarrow x\in\{-6,\ 1\}$

$\it b)\ \sqrt{x+2}\cdot\sqrt{x+3}=\sqrt{12}\\ \\ \sqrt{x+2} \Rightarrow x+2\geq0\ (condi\c{\it t}ie\ de\ existen\c{\it t}\breve a)\ \ \ \ \ (*)\\ \\ \sqrt{x+2}\cdot\sqrt{x+3}=\sqrt{12} \Rightarrow (x+2)(x+3)=12=3\cdot4=-4\cdot(-3)\stackrel{(*)}{\Longrightarrow}\\ \\ \Rightarrow x+2=3 \Rightarrow x=1\ \ (solu\c{\it t}ie\ \ unic\breve a)$