Find a if the coefficient of x^11 in the expansion of (x^2+1/ax)^10 is 15.

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Guest Nov 1, 2014

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Best Answer

The general term in this expansion can be written as nCr(10,10-n)(x²)ⁿ(1/ax)^10-n

When the power of x is 11 we must have 2n - (10 - n) = 11, which means that n = 7

nCr(10, 10-7) = 120 so given that nCr(10,10-n)/a^10-n = 15 we have 120/a³ = 15 or a³ = 120/15 = 8

So a = 2

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Alan Nov 1, 2014

Alan · Answer 1 · 2014-11-01T02:21:18

The general term in this expansion can be written as nCr(10,10-n)(x²)ⁿ(1/ax)^10-n

When the power of x is 11 we must have 2n - (10 - n) = 11, which means that n = 7

nCr(10, 10-7) = 120 so given that nCr(10,10-n)/a^10-n = 15 we have 120/a³ = 15 or a³ = 120/15 = 8

So a = 2

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