If 1 x^4+x^2+1 = A x+B x^2+x+1 + C x+D x^2-x+1 , then C+D is equal to

Step-by-step solution

Given, gathered 1 x^4+x^2+1 =- A x+B x^2+x+1 + C x+D x^2-x+1 1=(A x+B) (x^2-x+1 )+(C x+D) (x^2+x+1 ) 1= (A x^3+A x²⁺ A x+B x^2-B x+B ) + (C x^3+C x^2+C x+D x^2+D x+D ) 1=(A+C) x^3+(-A+B+C+D) x^2 +(A-B+C+D) x+(B+D) gathered On comparing, the coefficient of like powers on both sides, we get aligned A+C & =0 -A+B+C+D & =0 A-B+C+D & =0 B+D & =1 aligned and On adding Eqs. (ii) and (iii), we get aligned 2(C+D) & =0 C+D & =0 aligned