AP EAMCET · Maths · Binomial Theorem
If \(x>\sqrt{3}\) and \(\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}\) is expanded in terms of powers of \(x\), then the coefficient of \(\mathrm{x}^{-8}\) is
- A \(0\)
- B \(-81\)
- C \(46\)
- D \(-46\)
Answer & Solution
Correct Answer
(D) \(-46\)
Step-by-step Solution
Detailed explanation
\(\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)} = \frac{A}{x^2+2} + \frac{B}{x^2+3}\) \(A = \frac{(-2)+1}{(-2)+3} = -1\) \(B = \frac{(-3)+1}{(-3)+2} = 2\) \(= \frac{-1}{x^2+2} + \frac{2}{x^2+3}\)…
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