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The sum of the real values of x for which the middle term in the binomial expansion of ${(\frac{x^{3}}{3} + \frac{3}{x})}^{8}$ equals 5670 is

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Correct option is B

ln expansion of x33+3x8the middle term is T4+1[∵ here, n=8 which is even, therefore middle term =n+22th term ]∴ 5670=8C4x3343x4=8⋅7⋅6⋅51⋅2⋅3⋅4x8 ∵Tr+1=8Crx338−r3xr⇒ x8=34⇒x=±3So, sum of all values of x i.e +3 and −3=0

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The sum of the real values of x for which the middle term in the binomial expansion of x33+3x8 equals 5670 is

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The sum of the real values of x for which the middle term in the binomial expansion of ${(\frac{x^{3}}{3} + \frac{3}{x})}^{8}$ equals 5670 is