AP EAMCET · Maths · Basic of Mathematics
If \(\frac{x^4}{(x-1)(x-2)(x-3)}=A x+B \cdot \frac{1}{(x-1)}+C \cdot \frac{1}{(x-2)}+D \cdot \frac{1}{(x-3)}+E\), then \(A+B+C+D+E=\)
- A \(-12\)
- B \(6\)
- C \(18\)
- D \(32\)
Answer & Solution
Correct Answer
(D) \(32\)
Step-by-step Solution
Detailed explanation
\( \frac{x^4}{(x-1)(x-2)(x-3)} = x+6+\frac{25x^2-60x+36}{(x-1)(x-2)(x-3)} \) \( A=1, E=6 \) \( B = \left. \frac{25x^2-60x+36}{(x-2)(x-3)} \right|_{x=1} = \frac{25(1)^2-60(1)+36}{(-1)(-2)} = \frac{1}{2} \)…
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