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If the binomial expansion of  (a+b x)^{-2} \,is\,\, \frac{1}{4}-3 x+\ldots \ldots,where a>0, then (a, b) is

 

Option: 1

(2,12)


Option: 2

(2,8)


Option: 3

(-2,12)


Option: 4

None of these.


Answers (1)

best_answer

(a+b x)^{-2}=a^{-2}\left(1+\frac{b}{a} x\right)^{-2} \\

=\frac{1}{a^2}\left[1+(-2)\left(\frac{b}{a} x\right)+\ldots \ldots\right]=\frac{1}{a^2}-\frac{2 b}{a^3} x+\ldots . \\

 Also, (a+b x)^{-2}=\frac{1}{4}-3 x+\ldots .

\quad \frac{1}{a^2}=\frac{1}{4}  ...(1) \,\,and -\frac{2 b}{a^3}=-3\,\,...(2)

(1) \Rightarrow a^2=4 \Rightarrow a=2  and from (2) b=12

Posted by

himanshu.meshram

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