Question 20
The value of expression $$\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}$$ is.
Solution
Let us assume $$\sqrt{\ \sqrt{\ 5}+2}+\sqrt{\ \sqrt{\ 5}-2}=a$$.
Squaring both sides:
$$\left(\sqrt{\ 5}+2\right)+\left(\sqrt{\ 5}-2\right)+2\sqrt{\ \left(\sqrt{\ 5}+2\right)\left(\ \sqrt{\ 5}-2\right)}=2\sqrt{\ 5}+2=a^2$$
==> $$a\ =\ \sqrt{\ 2}\times\ \left(\sqrt{\ \sqrt{\ 5}+1}\right)$$
and, $$\frac{a}{\left(\sqrt{\ \sqrt{\ 5}+1}\right)}=\sqrt{\ 2}$$ i.e. Option B.
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