[tex]\displaystyle\bf\\Explicatie:\\\\Inversul~numarului~a~este~\frac{1}{a}\\\\Proprietate:\\\\ Produsul~dintre~un~numar~si~inversul~lui~este~egal~cu~1.\\\\a\times\frac{1}{a}=1\\\\Rezolvare:\\\\Inversul~lui~\sqrt{5}-2~este:\\\\\frac{1}{\sqrt{5}-2}\\\\Rationalizam~numitorul:\\\\\frac{\sqrt{5}+2}{(\sqrt{5}-2)(\sqrt{5}+2)}=\frac{\sqrt{5}+2}{5-4}=\frac{\sqrt{5}+2}{1}=\boxed{\bf\sqrt{5}+2}[/tex]
