Verified answer

[tex]\displaystyle\bf\\x^{2} -2x+2\sqrt{3}-3=0\\\\Teorema \ Vieta:\\x_{1}+x_{2} =2\\\\x_{1} \cdot x_{2} =2\sqrt{3} -3\\\\\\\frac{1}{x_{1} } +\frac{1}{x_{2} } =\frac{x_{1} +x_{2} }{x_{1} \cdot x_{2} } =\frac{2}{2\sqrt{3} -3}[/tex]