AP EAMCET · Maths · Binomial Theorem
If \((a+b x)^{-3}=\frac{1}{27}+\frac{1}{3} x+\ldots\), then the ordered pair \((a, b)\) equals to
- A \((3,-27)\)
- B \(\left(1, \frac{1}{3}\right)\)
- C \((3,9)\)
- D \((3,-9)\)
Answer & Solution
Correct Answer
(D) \((3,-9)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \text { Now, }(a+b x)^{-3} & =a^{-3}\left(1+\frac{b x}{a}\right)^{-3} \\ & =\frac{1}{a^3}\left(1-{ }^3 C_1\left(\frac{b x}{a}\right)+\ldots\right) \\ \Rightarrow \quad \frac{1}{a^3} & -{ }^3 C_1 \frac{1}{a^3}\left(\frac{b x}{a}\right)+\ldots \\ &…
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