The sum of the real values of x for which the middle term in the binomial expansion of ( x^33+ 3x)^8 equals 5670 is :

Question

Accepted Answer

Correct answer: A. (a) Middle term, ( n2+1)^ th term in the binomial expansion of ( x^33+ 3x)^8 is, T_4+1=8_C_4 ( x^33 )^4 ( 3x )^4=5670 ⇒ 8 7 6 54 3 2=x^12-4=5670 ⇒x^8=81 ⇒x^8-81=0 ∴ sum of all values of x= sum of roots of equation (x^8-81=0).

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

Solution

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