SOLUTION: Find the term in the expansion of {{{(2x + 1/x^2)^9}}} that does not contain x.
{{{(2x + 1/x^2)^9}}}=(2x + 1/x^2)^9
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-> SOLUTION: Find the term in the expansion of {{{(2x + 1/x^2)^9}}} that does not contain x.
{{{(2x + 1/x^2)^9}}}=(2x + 1/x^2)^9
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Question 1063342: Find the term in the expansion of that does not contain x.
=(2x + 1/x^2)^9 Found 2 solutions by stanbon, MathTherapy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find the term in the expansion of (2x + 1/x^2)^9 that does not contain x.
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Find (2x)^a*(x^-2)b = k*x^0
(2^a)[x^a*x^(-2b)] = k*x^0
(2^a)[x^(a-2b)] = k*x^0
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Determine a and b where
a-2b = 0
a+b = 9
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Subtract to get:: 3b = 9
b = 3
The a = 6
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Term:: 9C6(2x)^6(1/x^2)^3 = 84(64x^6)(x^-6) = 5376
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Cheers,
Stan H.
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