Question 6 - A-Level Maths

In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
1. Expand and simplify
$$\left( r - \frac { 1 } { r } \right) ^ { 2 }$$
Express $\frac { 1 } { 3 + 2 \sqrt { 2 } }$ in the form $p + q \sqrt { 2 }$ where $p$ and $q$ are integers.
Use the results of parts (a) and (b), or otherwise, to show that $$\sqrt { 3 + 2 \sqrt { 2 } } - \frac { 1 } { \sqrt { 3 + 2 \sqrt { 2 } } } = 2$$