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Question
Answer the following:
Show that there is no term containing x6 in the expansion of `(x^2 - 3/x)^11`
Solution
Here a = x2, b = `(-3)/x`, n = 11
We have, tr+1 = nCr, an–r .br
= `""^11"C"_"r" (x^2)^(11 - "r") ((-3)/x)^"r"`
= 11Cr x22–2r (-3)r (x–r)
= 11Cr (–3)r . x22–3r
To get the term x6, we must have
x22–3r = x6
∴ 23 – 3r = 6
∴ 3r = 16
∴ r = `16/3`, which is not possible
∴ there is no term containing x6 in the expansion of `(x^2 - 3/x)^11`.
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