AP EAMCET · Maths · Basic of Mathematics
If \(\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}\), then \(f(-2)+A+B=\)
- A \(32\)
- B \(28\)
- C \(22\)
- D \(20\)
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(\frac{x^4}{(x-1)(x-2)} = x^2+3x+7 + \frac{15x-14}{(x-1)(x-2)}\) \(f(x) = x^2+3x+7\) \(15x-14 = A(x-2)+B(x-1)\) \(x=1 \Rightarrow 1 = -A \Rightarrow A=-1\) \(x=2 \Rightarrow 16 = B\) \(f(-2) = (-2)^2+3(-2)+7 = 4-6+7 = 5\) \(f(-2)+A+B = 5+(-1)+16 = 20\)
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