Question

\(\sqrt{\dfrac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\dfrac{4}{\left(2+\sqrt{5}\right)^2}}\)

Answer 1

\(\sqrt{\dfrac{4}{\left(2-\sqrt{5}\right)^2}}-\sqrt{\dfrac{4}{\left(2+\sqrt{5}\right)^2}}\)

\(=\sqrt{\left(\dfrac{2}{2-\sqrt{5}}\right)^2}-\sqrt{\left(\dfrac{2}{2+\sqrt{5}}\right)^2}\)

\(=\left|\dfrac{2}{2-\sqrt{5}}\right|-\left|\dfrac{2}{2+\sqrt{5}}\right|\)

\(=\dfrac{2}{\sqrt{5}-2}-\dfrac{2}{2+\sqrt{5}}\)(vì \(\sqrt{5}>2\))

\(=\dfrac{4+2\sqrt{5}-2\sqrt{5}+4}{\left(\sqrt{5}\right)^2-2^2}\)

\(=\dfrac{8}{21}\)