AP EAMCET201822 Apr 2018Evening ShiftMathematicsIndefinite IntegrationActual
aligned & If 3 x^2+1 (x^2+1 ) (x^2+2 )^2 = A x+B x^2+1 + C x+D x^2+2 & + E x+F (x^2+2 )^2 , then A+C+E= aligned
Options
- A0
- B7 3
- C1
- D4 3
Correct answer
A. 0
Step-by-step solution
If array r 3 x^2+1 (x^2+1 ) (x^2+2 )^2 = A x+B x^2+1 + C x+D x^2+2 + E x+F (x^2+2 )^2 3 x^2+1 (x^2+1 ) (x^2+2 )^2 array aligned & A x+B (x^2+2 )^2+(C x+D) (x^2+1 ) = & (x^2+2 )+(E x+F) (x^2+1 ) (x^2+1 ) (x^2+2 )^2 aligned gathered 3 x^2+1=(A x+B) (x^2+2 )^2+(C x+D) (x^2+1 ) (x^2+2 )+(E x+F) (x^2+1 ) gathered On comparing the coefficient of different term, A=0, C=0 and E=0 So, A+C+E=0