CAIE P1 2022 June — Question 3

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
TopicBinomial Theorem (positive integer n)
TypeTwo equations from coefficients

3 The coefficient of \(x ^ { 4 }\) in the expansion of \(\left( 2 x ^ { 2 } + \frac { k ^ { 2 } } { x } \right) ^ { 5 }\) is \(a\). The coefficient of \(x ^ { 2 }\) in the expansion of \(( 2 k x - 1 ) ^ { 4 }\) is \(b\).
  1. Find \(a\) and \(b\) in terms of the constant \(k\).
  2. Given that \(a + b = 216\), find the possible values of \(k\).