thực hiện phép tính sau: $a,$ $(1+$$\frac{5-\sqrt{5} }{1-\sqrt{5}})$ $($$\frac{5+\sqrt{5} }{1+\sqrt{5}} $+1$)$

Đáp án:

 `a)`

`(1+\frac{5-\sqrt{5}}{1-\sqrt{5}}).(\frac{5+\sqrt{5}}{1+\sqrt{5}}+1)`

`=[1+\frac{\sqrt{5}.(\sqrt{5}-1)}{-(\sqrt{5}-1)}].[\frac{\sqrt{5}.(\sqrt{5}+1)}{\sqrt{5}+1}+1]`

`=[1+(-\sqrt{5})].(\sqrt{5}+1)`

`=(1-\sqrt{5}).(1+\sqrt{5})`

`=1^{2}-(\sqrt{5})^{2}`

`=1-5`

`=-4`