2024 IGCSE Additional Mathematics February/March 0606/22 Q10

2024 IGCSE Additional Mathematics February/March 0606/22 Q10

10 marks

The expansion of \(\left(a+\dfrac xa\right)^n\) in ascending powers of \(x\) begins \(b^4+48b^3x\), where \(n\), \(a\) and \(b\) are positive integers.

  1. Show that \(a^{\frac n2-4}=\left(\dfrac{48}{n}\right)^2\).[4]
  2. Given also that the third term is \(1056b^2x^2\), find the values of \(n\), \(a\) and \(b\).[6]

Solution:

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Answer:(a) \(a^{\frac n2-4}=\left(\dfrac{48}{n}\right)^2\). (b) \(n=12,\ a=4,\ b=64\).

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