[tex]\it \dfrac{a\sqrt3+2}{\sqrt3+b}=(1+\sqrt3)^2 \Rightarrow a\sqrt3+2=(\sqrt3+b)(4+2\sqrt3) \Rightarrow \\ \\ \\ \Rightarrow a\sqrt3+2=4\sqrt3+6+4b+2b\sqrt3 \Rightarrow a\sqrt3+2=\sqrt3(4+2b)+4b+6 \Rightarrow \\ \\ \Rightarrow 4b+6=2 \Rightarrow b=-1\ \ \ \ \ (*)\\ \\ a=4+2b\stackrel{(*)}{\Longrightarrow}\ a=4-2 \Rightarrow a=2[/tex]
Numerele cerute sunt: a = 2, b = -1 .
