AP EAMCET Engineering 2013 Solved Paper

Given,

1

x4+x2+1

=−

Ax+B

x2+x+1

+

Cx+D

x2−x+1

⇒1=(Ax+B)(x2−x+1) +(Cx+D)(x2+x+1)
⇒1=(Ax3+Ax2+Ax+Bx2−Bx+B) +(Cx3+Cx2+Cx+Dx2+Dx+D)
⇒ 1=(A+C)x3+(−A+B+C+D)x2 +(A−B+C+D)x+(B+D)
On comparing, the coefficient of like powers on both sides, we get
A+C=0 ...…(i)
−A+B+C+D=0 ......(ii)
A−B+C+D=0 .......(iii)
and B+D=1 ......(iv)
On adding Eqs. (ii) and (iii), we get
2(C+D)=0
⇒ C+D=0