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AP EAMCET202420 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

If A x-a + B x+C x^2+b^2 = 1 (x-a) (x^2+b^2 ) then C =

Options

  1. A-1 a^2+b^2
  2. B1 a^2+b^2
  3. C-a a^2+b^2
  4. Da a^2+b^2

Correct answer

C. -a a^2+b^2

Step-by-step solution

A (x-a) + B x+C x^2+b^2 = 1 (x-a) (x^2+b^2 ) A (x^2+b^2 )+(B x+C)(x-a)=1 (A+B) x^2+(C-a B) x+A b^2-a C=1 On comparing we get, A+B=0 ....(i) C-a B=0 ....(ii) A b^2-a C=1 ....(iii) From (i) and (ii), C+a A=0 A= -C a ; Put A= -C a in equation (iii), -C a b^2-a C=1 -C ( b^2+a^2 a )=1 C= -a a^2+b^2

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