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AP EAMCET202423 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

aligned & 4 x^2+5 (x-2)^4 = A (x-2) + B (X-2)^2 + C (X-2)^3 + D (X-2)^4 then & A C + B C + D C = aligned

Options

  1. A29 4
  2. B23 4
  3. C5 4
  4. D4 5

Correct answer

C. 5 4

Step-by-step solution

4 x^2+5 (x-2)^4 = A x-2 + B (x-2)^2 + C (x-2)^3 + D (x-2)^4 A(x-2)^3+B(x-2)^2+C(x-2)+D=4 x^2+5 If x=2 D=21 Co-efficient of x^3, A=0 Constant term, 4 B-2 C+21=5 4 B-2 C=-16 Co-efficient of x^2, B=4 So, 16-2 C=-16 C=16 Now, A C + B C + D C = A+B+D C = 4+21 16 = 5 4 .

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