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AP EAMCET · Maths · Straight Lines

If \(\frac{x^2+5 x+7}{(x-3)^3}+\frac{A}{(x-3)}+\left[\frac{B}{(x-3)^2}+\frac{C}{(x-3)^3}\right.\), then the equation of the line having slope \(A\) and passing through the point \((B, C)\) is

  1. A \(x+y-20=0\)
  2. B \(x-y+20=0\)
  3. C \(x+y+20=0\)
  4. D \(x-y-20=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(x-y+20=0\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} & \frac{x^2+5 x+7}{(x-3)^3}=\frac{A}{x-3}+\frac{B}{(x-3)^2}+\frac{C}{(x-3)^3} \\ \Rightarrow x^2+5 x+7 & =A(x-3)^2+B(x-3)+C \end{aligned} \] Put \(x=3\) in Eq. (i), we get \[ \begin{array}{rlrl} 9+15+7 & =C \\ \Rightarrow & & C & =31 \end{array} \]…