SPS SPS FM Pure 2021 May — Question 8

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2021
SessionMay
TopicHyperbolic functions

8.
  1. Using the definition of \(\sinh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\), show that $$4 \sinh ^ { 3 } x = \sinh 3 x - 3 \sinh x$$
  2. In this question you must show detailed reasoning. By making a suitable substitution, find the real root of the equation $$16 u ^ { 3 } + 12 u = 3$$ Give your answer in the form \(\frac { \left( a ^ { \frac { 1 } { b } } - a ^ { - \frac { 1 } { b } } \right) } { c }\) where \(a , b\) and \(c\) are integers.
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