Question

RÚT GỌN

a.\(\dfrac{1}{\sqrt{x+2\sqrt{x-1}}}+\dfrac{1}{\sqrt{x-2\sqrt{x-1}}}\)

b. \(\dfrac{1}{2\sqrt{3}+\sqrt{9+4\sqrt{5}}}-\dfrac{1}{2\sqrt{3}-\sqrt{9-4\sqrt{5}}}\)

Answer 1

a: \(=\dfrac{1}{\sqrt{x-1}+1}+\dfrac{1}{\sqrt{x-1}-1}\)

\(=\dfrac{\sqrt{x-1}-1+\sqrt{x-1}+1}{x-2}=\dfrac{2\sqrt{x-1}}{x-2}\)

b: \(=\dfrac{1}{2\sqrt{3}+\sqrt{5}+2}-\dfrac{1}{2\sqrt{3}-\sqrt{5}+2}\)

\(=\dfrac{1}{\left(2\sqrt{3}+2\right)+\sqrt{5}}-\dfrac{1}{\left(2\sqrt{3}+2\right)-\sqrt{5}}\)

\(=\dfrac{2\sqrt{3}+2-\sqrt{5}-2\sqrt{3}-2-\sqrt{5}}{11+8\sqrt{3}}\)

\(=\dfrac{-2\sqrt{5}}{11+8\sqrt{3}}=\dfrac{\sqrt{5}\left(22-16\sqrt{3}\right)}{71}\)