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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 260

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+3p​4+27p​​

Show 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+3p​​
[4]
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3 Unit A2 1: Pure Mathematics (A-level only) Questions

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