How do we solve question no 2

Dear Student ,

Please find below the solution to the asked query :

N = \frac{\sqrt{\sqrt{5} + 2} + \sqrt{\sqrt{5} - 2}}{\sqrt{\sqrt{5} + 1}} - \sqrt{3 - 2 \sqrt{2}} Let x = \sqrt{\sqrt{5} + 2} + \sqrt{\sqrt{5} - 2} x^{2} = {(\sqrt{\sqrt{5} + 2} + \sqrt{\sqrt{5} - 2})}^{2} = \sqrt{5} + 2 + \sqrt{5} - 2 + 2 (\sqrt{\sqrt{5} + 2}) (\sqrt{\sqrt{5} - 2}) = 2 \sqrt{5} + 2 \sqrt{{(\sqrt{5})}^{2} - 2^{2}} = 2 \sqrt{5} + 2 \sqrt{5 - 4} = 2 \sqrt{5} + 2 x^{2} = 2 (\sqrt{5} + 1) x = \sqrt{2} \sqrt{\sqrt{5} + 1} Now, N = \frac{\sqrt{2} \sqrt{\sqrt{5} + 1}}{\sqrt{\sqrt{5} + 1}} - \sqrt{3 - 2 \sqrt{2}} = \sqrt{2} - \sqrt{2 + 1 - 2 (1) (\sqrt{2})} = \sqrt{2} - \sqrt{{(\sqrt{2})}^{2} + 1^{2} - 2 (1) (\sqrt{2})} = \sqrt{2} - \sqrt{{(\sqrt{2} - 1)}^{2}} = \sqrt{2} - \sqrt{2} + 1 = 1 ANS . . .

Hence, option (A) is correct.

Regards