3.105: Binomial terms equal

0606/23/O/N/24 — Question 7 · 7 marks

(a)
In the expansion of (x+x2)8(x+x^{2})^{8} in ascending powers of xx, the 3rd and 6th terms are equal. Find the value of xx.
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(b)(i)
In the expansion of (x+2x)n\left(x+\dfrac{2}{x}\right)^{n} in decreasing powers of xx, the 6th term is a constant. Find the value of the positive integer nn.
[2]
(b)(ii)
Find the value of the 6th term.
[2]