Simplify using given results

A question is this type if and only if it asks to use results from previous parts to prove or simplify a more complex expression, such as using (r - 1/r)^2 and 1/(3 + 2√2) to show a specific identity.

1 questions · Moderate -0.8

Sort by: Default | Easiest first | Hardest first
Edexcel P1 2023 June Q6
7 marks Moderate -0.8
  1. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
    1. Expand and simplify
    $$\left( r - \frac { 1 } { r } \right) ^ { 2 }$$
  2. Express \(\frac { 1 } { 3 + 2 \sqrt { 2 } }\) in the form \(p + q \sqrt { 2 }\) where \(p\) and \(q\) are integers.
  3. Use the results of parts (a) and (b), or otherwise, to show that $$\sqrt { 3 + 2 \sqrt { 2 } } - \frac { 1 } { \sqrt { 3 + 2 \sqrt { 2 } } } = 2$$