Question

The middle term in the expansion of (x+b/x)∧6 is 160 then b=? a) 8 b)6 c)2 d)4

Answer 1

Answer:

a)4...

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

1)

$\bigg( \: \sf x + \dfrac{ b}{x} \bigg)$

Total term = 7

$\sf \: Middle \: term =\dfrac{7+1}{2}=\dfrac{8}{2}=4^th$

$\sf \: T_{4}= \: ^6C_{3} \: \: \: x^3 \: \: \: \: \bigg (\dfrac{b}{x}\bigg ) ^3$

$\sf \: 160 = \dfrac{6!}{3!3!} .x {}^{3 } \: \: \dfrac{b {}^{3} }{x {}^{3} }$

$\sf \: {b}^{3} = 8$

$\implies \sf \color{darkgreen}{b =2}$

Hence, option(c) is correct