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  4. The sum of the real values of x for which the middle term in the binomial expansion of ((x3/3) + (3/x))8 equals 5670 is :

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

JEE MainJEE Main 2019Binomial Theorem

Solution:

$T_{5} =^{8}C_{4} \frac{x^{12}}{81} \times\frac{81}{x^{4}} = 5670 $
$ \Rightarrow 70x^{8} = 5670 $
$ \Rightarrow x = \pm \sqrt{3} $