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TS EAMCET · Maths · Quadratic Equation

\(\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \ & \Rightarrow A+C=\end{aligned}\)

  1. A 4
  2. B 5
  3. C 6
  4. D 8
Verified Solution

Answer & Solution

Correct Answer

(D) 8

Step-by-step Solution

Detailed explanation

Given, \(\begin{array}{r}\frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2} \\ +\frac{C}{x-3}\end{array}\) \(\begin{aligned} \Rightarrow x^2+x & +1=A(x-2)(x-3) \\ & +B(x-1)(x-3)+C(x-1)(x-2)\end{aligned}\) Put \(x=1,2\) and 3 respectively we get…