Question 25
Find the value of $W^2-2W$ where
$$W=\frac{\sqrt{100+\sqrt1}+\sqrt{100+\sqrt2}+\cdots+\sqrt{100+\sqrt{9999}}}{\sqrt{100-\sqrt1}+\sqrt{100-\sqrt2}+\cdots+\sqrt{100-\sqrt{9999}}}.$$
$$W=\frac{\sqrt{100+\sqrt1}+\sqrt{100+\sqrt2}+\cdots+\sqrt{100+\sqrt{9999}}}{\sqrt{100-\sqrt1}+\sqrt{100-\sqrt2}+\cdots+\sqrt{100-\sqrt{9999}}}.$$