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  • Solve it, - The sum of the real values of x for which the middle term in the binomial expansion of equals 576 - Binomial theorem and its simple applications - JEE Main

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  5760 is :

  • Option 1)

    6

  • Option 2)

    4

  • Option 3)

    0

  • Option 4)

    8

Answers (1)

best_answer

 

Middle term in Binomial Expression if n is even -

In the expression of 

\left ( x+a \right )^{n}:^{n}c_{\frac{n}{2}}\cdot x^{\frac{n}{2}}\cdot y^{\frac{n}{2}} is

middle term if n is even

 

- wherein

where \left ( \frac{n}{2}+1 \right ) th term is middle term

 

Middle Term can be written as 

T_{5}=^{8}C_{4}\left ( \frac{3}{x} \right )^{3}\left ( \frac{x^{2}}{3} \right )^{4}=5670

\Rightarrow 70x^{8}=5670

\Rightarrow x^{8}=81

\Rightarrow x^{2}=\pm \sqrt{3}

sum of real values =0

 


Option 1)

6

Option 2)

4

Option 3)

0

Option 4)

8

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