Question

rut gon C= \((\dfrac{1-\sqrt{3}}{1+\sqrt{3}}-\dfrac{1+\sqrt{3}}{1-\sqrt{3}}):\sqrt{108}\)

Answer 1

\(C=\left(\dfrac{1-\sqrt{3}}{1+\sqrt{3}}-\dfrac{1+\sqrt{3}}{1-\sqrt{3}}\right):\sqrt{108}\)

= \(\dfrac{\left(1-\sqrt{3}\right)^2-\left(1+\sqrt{3}\right)^2}{\left(1+\sqrt{3}\right)\left(1-\sqrt{3}\right)}:6\sqrt{3}\)

= \(\dfrac{1-2\sqrt{3}+3-1-2\sqrt{3}-3}{1-3}.\dfrac{1}{6\sqrt{3}}\)

= \(\dfrac{-4\sqrt{3}}{-2}.\dfrac{1}{6\sqrt{3}}\)

= \(\dfrac{2\sqrt{3}}{6\sqrt{3}}=\dfrac{1}{3}\)