The sum of the real values of x for which the middle term in the binomial expansion ofx33+3x8 equal 5670 is

Solution:

Given binomial expansion is ${(\frac{x^{3}}{3} + \frac{3}{x})}^{8}$ So, middle term $T_{5} =^{8} C_{4} {(\frac{x^{3}}{3})}^{4} \cdot {(\frac{3}{x})}^{4} = 5670$

$\begin{array}{l} \Rightarrow^{8} C_{4} \frac{x^{12}}{3^{4}} \cdot \frac{3^{4}}{x^{4}} = 5670 \\ \Rightarrow 70 x^{8} = 5670 \Rightarrow x^{8} = 81 \Rightarrow x = \pm \sqrt{3} \end{array}$

$∴$ Sum of real values of x is 0.

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