# Appearance may deceive.

Level pending

$$p$$ and $$q$$ are real numbers where

$$p=\sqrt{\frac{17}{2}+6\sqrt{2}}+\sqrt{\frac{17}{2}-6\sqrt{2}}$$

and

$$q=\sqrt{\frac{17}{2}+6\sqrt{2}}-\sqrt{\frac{17}{2}-6\sqrt{2}}$$.

Then $$\sqrt{2} (pq)^{-1}$$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are coprime integers.

What is the value of $$a+b$$?

×