1. Zadatak

Svođenjem na zajednički nazivnik izračunat ćemo vrijednost izraza $A$.

$$\begin{aligned} A&=\frac{\sqrt{2022}+1}{\sqrt{2022}-1}-\frac{2}{\sqrt{2022}+1}\\ &=\frac{(\sqrt{2022}+1)^2-2(\sqrt{2022}-1)}{(\sqrt{2022}-1)(\sqrt{2022}+1)}\\ &=\frac{2022+2\sqrt{2022}+1-2\sqrt{2022}+2}{2022-1}\\ &=\frac{2025}{2021}. \end{aligned}$$

Tada je:

$$\sqrt{1-A^{-1}}=\sqrt{1-\frac{2021}{2025}}=\sqrt{\frac4{2025}}=\frac2{45}.$$