TS EAMCET · Maths · Quadratic Equation
\(\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \ & \Rightarrow A+C=\end{aligned}\)
- A 4
- B 5
- C 6
- D 8
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…
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