JEE MAIN - Mathematics (2019 - 11th January Morning Slot - No. 12)
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 :
0
8
6
4
Explanation
$${T_5} = {}^8{C_4}{{{x^{12}}} \over {81}} \times {{81} \over {{x^4}}} = 5670$$
$$ \Rightarrow 70{x^8} = 5670$$
$$ \Rightarrow x = \pm \sqrt 3 $$
$$ \Rightarrow 70{x^8} = 5670$$
$$ \Rightarrow x = \pm \sqrt 3 $$
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