Question

как помогите пожалуйста ))))!!​

Answer 1

$\sqrt{21-8\sqrt5}+\frac{1}{\sqrt5-2}=\sqrt{16+5-2\cdot 4\sqrt5}+\frac{1}{\sqrt5-2}=\\\\=\sqrt{(4-\sqrt5)^2}+\frac{1}{\sqrt5-2}=|\underbrace {4-\sqrt5}_{>0}|+\frac{1}{\sqrt5-2}=(4-\sqrt5)+\frac{1}{\sqrt5-2}=\\\\=4-\sqrt5+\frac{\sqrt5+2}{(\sqrt5-2)(\sqrt5+2)}=4-\sqrt5+\frac{\sqrt5+2}{5-4}=4-\sqrt5+\sqrt5+2=6$