If 1 x^4+1 = A x+B x^2+ 2 x+1 + C x+D x^2- 2 x+1 then B D-A C=

Step-by-step solution

Since, given aligned & 1 x^4+1 = A x+B x^2+ 2 x+1 + C x+D x^2- 2 x+1 & (A x+B) (x^2- 2 x+1 )+(C x+D) (x^2+ 2 x+1 )=1 aligned If x=0 B+D=1 Equating co-efficient of x^3 A+C=0 Equating co-efficient of x^2 B- 2 A+D+ 2 C=0 1+ 2 (C-A)=0 A-C= 1 2 Aftersolving A+C=0 and A-C= 1 2 A= 1 2 2 , C= -1 2 2 Equating co-efficient of x A- 2 B+C+ 2 D=0 B-D=0 B= 1 2 , D= 1 2 Now, B D-A C 1 4 + 1 8 = 3 8 .