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AP EAMCET202123 Aug 2021Evening ShiftMathematicsIndefinite IntegrationActual

If 1 (3-5 x)(2+3 x) = A 3-5 x + B 2+3 x , then A+B is equal to

Options

  1. A7 19
  2. B8 19
  3. C9 19
  4. D10 19

Correct answer

B. 8 19

Step-by-step solution

Given, 1 (3-5 x)(2+3 x) = A 3-5 x + B 2+3 x 1 (3-5 x)(2+3 x) = 2 A+3 A x+3 B-5 B x (3-5 x)(2+3 x) 1=x(3 A-5 B)+(2 A+3 B)3 A-5 B=0 ...(i) and 2 A+3 B=1 ...(ii) Eq. (i) 3+ Eq. (ii) 59 A-15 B=0 10 A+15 B=5 19 A=5 A= 5 19 , B= ( 1-2 A 3 ) B= 3 19 A+B= 5 19 + 3 19 = 8 19

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