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 Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 100 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) 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.