In the design of a custom optical lens, the focal length FFF is calculated as the arithmetic mean of a rational base length LLL and an irrational correction factor γ\gammaγ.
Given that F=L+γ2F = \frac{L + \gamma}{2}F=2L+γ, prove by contradiction that the focal length FFF must be an irrational number.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
