[tex]\displaystyle\\
c=(2x+3)^2 -(2x+3)(2x-3) =\\\\= (2x+3)[(2x+3)-(2x-3)] =\\\\
=(2x+3)[\underline{2x}+3-\underline{2x}+3] =\\\\
= (2x+3)(3+3)=6(2x+3)=\boxed{\bf12x+18}\\\\
c = 12x+18 ~~\text{si}~~x = \sqrt{3} ~~\Longrightarrow~~c = \boxed{\bf12\sqrt{3}+18}\\\\
c=a\sqrt{3} +b\\\\
12\sqrt{3}+18 = a\sqrt{3} +b\\\\
\Longrightarrow\Longrightarrow\\\\
12\sqrt{3}=a\sqrt{3} ~~\Longrightarrow~~a = \frac{12\sqrt{3}}{\sqrt{3}} = \boxed{\bf12}\\\\
18 = b ~~\Longrightarrow~~ b = \boxed{\bf 18}[/tex]
