SPS SPS FM 2022 January — Question 5

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2022
SessionJanuary
TopicGeneralised Binomial Theorem
TypeTwo unknowns from two coefficient conditions

5.
  1. Expand \(( 1 + a x ) ^ { - 4 }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).
  2. The coefficients of \(x\) and \(x ^ { 2 }\) in the expansion of \(( 1 + b x ) ( 1 + a x ) ^ { - 4 }\) are 1 and - 2 respectively. Given that \(a > 0\), find the values of \(a\) and \(b\).
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