If \(x - \dfrac{1}{x} = u\), express \(x^3 - \dfrac{1}{x^3}\) and \(x^5 - \dfrac{1}{x^5}\) in terms of \(u\).
What happens if we square \(u\)?
Counting & Binomials
Suggestion
If \(x - \dfrac{1}{x} = u\), express \(x^3 - \dfrac{1}{x^3}\) and \(x^5 - \dfrac{1}{x^5}\) in terms of \(u\).
What happens if we square \(u\)?