ExamBro
ExamBro
TS EAMCET · Maths · Basic of Mathematics

If \(\frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5}\), then \((A, B, C)\) equals to

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

Answer & Solution

Correct Answer

(C) \((1,0,1)\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {Given, } \frac{2 x^3+x^2-5}{x^4-25}=\frac{A x+B}{x^2-5}+\frac{C x+1}{x^2+5} \\ & \therefore 2 x^3+x^2-5=(A x+B)\left(2 x^2+5\right) \\ & +(C x+1)\left(x^2-5\right) \\ & \Rightarrow 2 x^3+x^2-5=A x^3+5 A x+B x^2+5 B \\ & +C x^3-5 C x+x^2-5 \\ &…