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 :

• A. 6
• B. 8
• C. 0
• D. 4

Answer 1

Answer: (C)

$T_5{=}^8{C}_4\frac{x^{12}}{81}\times \frac{81}{x^4}=5670$
$\Rightarrow 70x^8=5670$
$\Rightarrow x=\pm \sqrt{3}$