Question

tính \(\dfrac{1}{\sqrt{1}-\sqrt{2}}+\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}\)

Answer 1

\(\dfrac{1}{\sqrt{1}-\sqrt{2}}+\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}\)

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

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

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

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

\(=-3-2\sqrt{2}-2\sqrt{3}\)