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.
132 exam-style questions on OCR (MEI) A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Disproof by counter example, 1.1.3 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.