( √3 - x)( √3 +x)< 4 -( √3 – x)^2

[latex]( sqrt{3} - x)( sqrt{3} +x) extless 4 -( sqrt{3} - x)^2\ 3-x^2 extless 4-(3-2sqrt{3}x+x^2)\ 3-x^2 extless 4-3+2sqrt{3}x-x^2\ 3 extless 1+2sqrt{3}x\ 2 extless 2sqrt{3}x\ 2sqrt{3}x extgreater 2 /:(2sqrt{3})\ x extgreater frac{1}{sqrt{3}}*frac{sqrt{3}}{sqrt{3}}=frac{sqrt{3}}{3}\ x extgreater frac{sqrt{3}}{3}\ \ oxed{xin(sqrt{3};+infty)}[/latex]