If x^2-7 x+2 x^4+3 x^2+4 = A x+B x^2+a x+2 + C x+D x^2+b x+2 and a>b then B + D =

Step-by-step solution

x^2-7 x+2 x^4+3 x^2+4 = A x+B x^2+a x+2 + C x+D x^2+b x+2 ...(i) x^2-7 x+2 x^4+3 x^2+4 = x^2-7 x+2 (x^2+x+2 ) (x^2-x+2 ) The form of the partial fraction decomposition is : x^2-7 x+2 (-x^2-x+2 ) (x^2+x+2 ) = P x+Q x^2-x+2 + R x+S x^2+x+2 ...(ii) aligned & x^2-7 x+2=(P x+Q) (x^2+x+2 )+(R x+S) & (x^2-x+2 ) & x^2-7 x+2=x^3(P+R)+x^2(-P+Q+R+S)+x(2 P & -Q+2 R+S)+(2 Q+2 S) aligned So, by comparing both sides, we get: aligned & P+R=0 & -P+Q+R+S=1 aligned 2 P-Q+2 R+S=-72 Q +2 ~S =2 ...(iii) Solving system (iii), we get: P=0