If N=(√(√(5)+2)+√(√(5)-2))/(√(√(5)+1))-√(3-2 √(2)), then the value of N is · ABC26GN1962

Let $X=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$. Then $X^{2}=\frac{(\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2})^{2}}{(\sqrt{\sqrt{5}+1})^{2}}$ $$\begin{aligned} & =\frac{(\sqrt{5}+2)+(\sqrt{5}-2)+2 \sqrt{(\sqrt{5}+2)(\sqrt{5}-2)}}{(\sqrt{5}+1)} \\ & =\frac{2 \sqrt{5}+2 \sqrt{(\sqrt{5})^{2}-(2)^{2}}}{\sqrt{5}+1}=\frac{2 \sqrt{5}+2}{\sqrt{5}+1} \\ & =\frac{2(\sqrt{5}+1)}{(\sqrt{5}+1)}=2 \end{aligned} \begin{aligned} \Rightarrow & X & =\sqrt{2} . \\ \therefore & N & =\sqrt{2}-\sqrt{3-2 \sqrt{2}}=\sqrt{2}-\sqrt{(\sqrt{2})^{2}+1^{2}-2 \times \sqrt{2} \times 1} \\ & & =\sqrt{2}-\sqrt{(\sqrt{2}-1)^{2}}=\sqrt{2}-(\sqrt{2}-1)=1 . \end{aligned}$$