Question

Ruút gọn A=\(\dfrac{1}{\sqrt{5}+1}-\sqrt[3]{\left(2-\sqrt{5}\right)^3}\)

Answer 1

`A=1/[\sqrt{5}+1]-\root{3}{(2-\sqrt{5})^3}`

`A=[\sqrt{5}-1]/[5-1]-(2-\sqrt{5})`

`A=[\sqrt{5}-1-4(2-\sqrt{5})]/4`

`A=[\sqrt{5}-1-8+4\sqrt{4}]/4`

`A=[5\sqrt{5}-9]/4`

Answer 2

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

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

    \(=\dfrac{1-2\sqrt{5}-2+5+\sqrt{5}}{\sqrt{5}+1}=\dfrac{4-\sqrt{5}}{\sqrt{5}+1}\)

    \(=\dfrac{\left(4-\sqrt{5}\right)\cdot\left(\sqrt{5}-1\right)}{\left(\sqrt{5}+1\right)\cdot\left(\sqrt{5}-1\right)}=\dfrac{4\sqrt{5}-4-5+\sqrt{5}}{5-1}=\dfrac{5\sqrt{5}-9}{4}\)