\(C=\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}+\sqrt{7-4\sqrt{3}}+\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
\(=\left(\dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}}+\dfrac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\right)+\left(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\right)\)
\(=\left[\dfrac{\left(\sqrt{7}-\sqrt{3}\right)^2}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}+\dfrac{\left(\sqrt{7}+\sqrt{3}\right)^2}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}\right]+\left(\sqrt{4-4\sqrt{3}+3}+\sqrt{4+4\sqrt{3}+3}\right)\)
\(=\dfrac{\left(\sqrt{7}-\sqrt{3}\right)^2+\left(\sqrt{7}+\sqrt{3}\right)^2}{\left(\sqrt{7}-\sqrt{3}\right)\left(\sqrt{7}+\sqrt{3}\right)}+\left[\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{2^2+2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}\right]\)
\(=\dfrac{7-2\sqrt{7}.\sqrt{3}+3+7+2\sqrt{7}.\sqrt{3}+3}{7-3}+\left[\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(2+\sqrt{3}\right)^2}\right]\)
\(=\dfrac{20}{4}+\left(\left|2-\sqrt{3}\right|+\left|2+\sqrt{3}\right|\right)\)
\(=5+2-\sqrt{3}+2+\sqrt{3}\) (vì \(2-\sqrt{3}>0,\) \(2+\sqrt{3}>0\))
\(=9\)
