Question

Giúp mk bài 1 ah

Answer 1

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

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

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

Answer 2

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

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

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

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