2024 IGCSE Additional Mathematics October/November 0606/23 Q7

2024 IGCSE Additional Mathematics October/November 0606/23 Q7

7 marks
  1. In the expansion of \((x+x^2)^8\) in ascending powers of \(x\), the 3rd and 6th terms are equal. Find the value of \(x\).[3]
  2. In the expansion of \(\left(x+\dfrac2x\right)^n\) in decreasing powers of \(x\), the 6th term is a constant.
    1. Find the value of the positive integer \(n\).[2]
    2. Find the value of the 6th term.[2]

Solution:

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Answer:(a) Expected nonzero value \(\sqrt[3]{\dfrac12}\); \(0\) also satisfies the printed equality. (b)(i) \(n=10\); (ii) \(8064\).

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