(2x^2+1/√x)^10
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2009-01-01 6:57 pm
Find the constant term and the term in x^9 in the expansion of
(2x^2+1/√x)^10
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(2x^2+1/√x)^10
唔該教教我^_^
回答 (1)
2009-01-01 7:30 pm
✔ 最佳答案
(2x2 + 1/√x)10 = (2x2)10 + 10C1(2x2)9(1/√x)1 + ...... + 10Cr(2x2)10-r(1/√x)r + ...... + (1/√x)10
General term in expansion
= 10Cr(2x2)10-r(1/√x)r
= 10Cr(2)10-rx20-2rx-r/2
= 10Cr(2)20-rx20-2.5r
Consider the constant term:
x20-2.5r = xo
20 - 2.5r = 0
2.5r = 20
r = 8
Constant term
= 10C8(2)20-(8)x20-2.5(8)
= (45)212
= 184320
Consider the x9 term:
x20-2.5r = x9
20 - 2.5r = 9
2.5r = 11
r = 4.4
r is not an integer.
There is no x9 term.
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