a) \(\dfrac{\sqrt{7}+5}{\sqrt{7}-5}+\dfrac{\sqrt{7}-5}{\sqrt{7}+5}\)
\(=\dfrac{\left(\sqrt{7}+5\right)^2}{\left(\sqrt{7}-5\right)\left(\sqrt{7}+5\right)}+\dfrac{\left(\sqrt{7}-5\right)^2}{\left(\sqrt{7}+5\right)\left(\sqrt{7}-5\right)}\)
\(=\dfrac{\left(\sqrt{7}+5\right)^2+\left(\sqrt{7}-5\right)^2}{\left(\sqrt{7}-5\right)\left(\sqrt{7}+5\right)}\)
\(=\dfrac{\left(7+10\sqrt{7}+25\right)+\left(7-10\sqrt{7}+25\right)}{7-25}\)
\(=\dfrac{14+50}{7-25}\)
\(=\dfrac{64}{-18}\)
\(=\dfrac{-32}{9}\)
b) \(\sqrt{12}+\sqrt{48}-\sqrt{\left(\sqrt{75}-\sqrt{108}\right)^2}\)
\(=\sqrt{12}+\sqrt{48}-\left|\sqrt{75}-\sqrt{108}\right|\)
\(=\sqrt{12}+\sqrt{48}-\left(\sqrt{108}-\sqrt{75}\right)\) ( Vì \(\sqrt{75}< \sqrt{108}\) )
\(=\sqrt{12}+\sqrt{48}-\sqrt{108}+\sqrt{75}\)
\(=2\sqrt{3}+4\sqrt{3}-6\sqrt{3}+5\sqrt{3}\)
\(=5\sqrt{3}\)
a)\(\dfrac{\sqrt{7}+5+\sqrt{7}-5}{\sqrt{7}-5}=\dfrac{2\sqrt{7}}{\sqrt{7}-5}=\dfrac{-7-5\sqrt{7}}{9}\approx-2,25\)
