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Question
Answer the following:
If the middle term in the expansion of `(x + "b"/x)^6` is 160, find b
Solution
There are 7 terms in the expansion of `(x + "b"/x)^6`.
∴ middle term = t4
We know that, in the expansion of (a+ b)n,
tr+1 = nCr, an–r br
Here a = x, b = `"b"/x`, n = 6 and fr t4, r = 3
∴ middle term = t4 = `""^6"C"_3 (x)^(6 - 3) ("b"/x)^3`
= `(6 xx 5 xx 4)/(1 xx 2 xx 3) xx x^3 xx "b"^3/"x"^3`
= 20b3
But, middle term = 160
∴ 20b3 = 160
∴ b3 = 8
∴ b = 2
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