A) 8
B) 6
C) 0
D) 4
Correct Answer: C
Solution :
Given binomial expansion is\[{{\left( \frac{{{x}^{3}}}{3}+\frac{3}{x} \right)}^{8}}\] So, middle term \[{{T}_{5}}{{=}^{8}}{{C}_{4}}{{\left( \frac{{{x}^{3}}}{3} \right)}^{4}}.{{\left( \frac{3}{x} \right)}^{4}}=5670\] \[\Rightarrow \]\[^{8}{{C}_{4}}\frac{{{x}^{12}}}{{{3}^{4}}}.\frac{{{3}^{4}}}{{{x}^{4}}}=5670\] \[\Rightarrow \]\[70{{x}^{8}}=5670\] \[\Rightarrow \]\[{{x}^{8}}=81\]\[\Rightarrow \]\[x=\pm \sqrt{3}\] \[\therefore \]Sum of real values of x is 0.
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