Question:
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 :
Correct Option: , 3
Solution:
$\mathrm{T}_{5}={ }^{8} \mathrm{C}_{4} \frac{\mathrm{x}^{12}}{81} \times \frac{81}{\mathrm{x}^{4}}=5670$
$\Rightarrow 70 x^{8}=5670$
$\Rightarrow x=\pm \sqrt{3}$
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