SOLUTION: Finds the coefficient of x^2 in the expansion of (x + (2/radical x))^8

Question 261557: Finds the coefficient of x^2 in the expansion of (x + (2/radical x))^8
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Finds the coefficient of x^2 in the expansion of (x + (2/radical x))^8
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(x + 2x^-1)^8
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Examine (x)^k(2x^(-1))^(n-k) = x^2
(x^k)(x^(k-n)) = x^2
x^(2k-n) = x^2
2k-n = 2
n = 2k-2
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8C8(x^0)(2x^-1)^8 = x^-8
8C7(x^1)(2x^-1)^7 = x^-6
8C6(x^2)(2x^-1)^6 = x^-2
...
8C5(x^3)(2x^-1)^5 = x
8C3(x^5)(2x^-1)^3 = 8x^2
...
8C1(x^2)^7(2x^-1)^1 = x^1
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Ans: 8
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Cheers,
Stan H.

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