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Question Number 113261 by Aina Samuel Temidayo last updated on 12/Sep/20

$$\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}$$

Answered by som(math1967) last updated on 12/Sep/20

$$\mathrm{let}\mathrm{p}=\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}$$$${\mathrm{p}}^2=\sqrt{5}+2+\sqrt{5}-2+2\sqrt{{\left(\sqrt{5}\right)}^2-2^2}$$$${\mathrm{p}}^2=2(\sqrt{5}+1)$$$$\therefore \mathrm{p}=\sqrt{2}\sqrt{\sqrt{5}+1}$$$$\therefore \frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{2+1-2\sqrt{2}}$$$$=\frac{\sqrt{2}\sqrt{\sqrt{5}+1}}{\sqrt{\sqrt{5}+1}}-\sqrt{{(\sqrt{2}-1)}^2}$$$$=\sqrt{2}-\sqrt{2}+1=1\mathrm{ans}$$

Commented by Aina Samuel Temidayo last updated on 12/Sep/20

$$\mathrm{Thanks}.$$

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