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AP EAMCET · Maths · Basic of Mathematics

If \(\frac{5 x^2+2}{x^3+x}=\frac{A_1}{x}+\frac{A_2 x+A_3}{x^2+1}\), then \(\left(A_1, A_2, A_3\right)=\)

  1. A (0, 2, 3)
  2. B (3, 0, 2)
  3. C (2, 3, 0)
  4. D (2, 0, 3)
Verified Solution

Answer & Solution

Correct Answer

(C) (2, 3, 0)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {Given that, } \frac{5 x^2+2}{x^3+x}=\frac{A_1}{x}+\frac{A_2 x+A_3}{x^2+1} \\ & \Rightarrow \frac{5 x^2+2}{x\left(x^2+1\right)}=\frac{A_1\left(x^2+1\right)+\left(A_2 x+A_3\right) x}{x\left(x^2+1\right)} \\ & \Rightarrow 5 x^2+2=A_1\left(x^2+1\right)+A_2…