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The sum of the real values of x for which the middle term in t

Question

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:

6

8

0

4

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Noah Discussed

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:

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Given

(\frac{x ^{3}}{3} + \frac{3}{x})^{8}

General term

= T_{r + 1} =^{8} C_{r} (\frac{x ^{3}}{3})^{8 - r} (\frac{3}{x})^{r}

Since n is even then the middle term is when

r = \frac{n}{2}

Here,

\frac{n}{2} = \frac{8}{2} = 4

T_{5} =^{8} C_{4} \frac{x ^{12}}{81} \times \frac{81}{x ^{4}} = 5670

\Rightarrow 70 x^{8} = 5670

\Rightarrow x = \pm 3

Hence, The sum of the real values of x are

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Question Text	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:
Answer Type	Text solution:1
Upvotes	150