In a structural analysis model, the stability ratio σ\sigmaσ of a cantilever beam depends on a load factor ppp, where p>13p > \frac{1}{3}p>31. The ratio is given by:
σ=4+27p1+3p \sigma = \frac{4 + \sqrt{27p}}{1 + \sqrt{3p}} σ=1+3p4+27pShow that this expression can be written in the form:
σ=9p−4+3p3p−1 \sigma = \frac{9p - 4 + \sqrt{3p}}{3p - 1} σ=3p−19p−4+3p368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.