The sum of the real values of x for which the middle term in the binomial expansion of [( …

Question

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

Accepted Answer

$${T_5} = {}^8{C_4}{{{x^{12}}} \over {81}} \times {{81} \over {{x^4}}} = 5670$$

$$ \Rightarrow 70{x^8} = 5670$$

$$ \Rightarrow x =  \pm \sqrt 3 $$

Solutions · 1