Summer Clouds
15/06/2017 at 09:00-
\(\dfrac{3+\sqrt{5}}{3-\sqrt{5}}+\dfrac{3-\sqrt{5}}{3+\sqrt{5}}=\dfrac{\left(3+\sqrt{5}\right)^2+\left(3-\sqrt{5}\right)^2}{\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)}\)
\(=\dfrac{9+6\sqrt{5}+5+9-6\sqrt{5}+5}{9-5}=\dfrac{28}{4}=7\)
Summer Clouds selected this answer. -
Thu Thảo 17/06/2017 at 21:50\(\dfrac{3+\sqrt{5}}{3-\sqrt{5}}+\dfrac{3-\sqrt{5}}{3+\sqrt{5}}\)
\(=\dfrac{\left(3+\sqrt{5}\right)^2}{9-5}+\dfrac{\left(3-\sqrt{5}\right)^2}{9-5}\)
\(=\dfrac{\left(3+\sqrt{5}+3-\sqrt{5}\right)\left(3+\sqrt{5}-3+\sqrt{5}\right)}{4}\)
\(=\dfrac{6\cdot2\sqrt{5}}{4}=\dfrac{12\sqrt{5}}{4}=3\sqrt{5}\)