If x 4 + 24 x 2 + 28 x 2 + 1 3 = A x + B x 2 + 1 + C x + D x 2 + 1 2 + E x + F x 2 + 1 3 then the value of A + B + C + D + E + F =

Step-by-step solution

Given x 4 + 24 x 2 + 28 x 2 + 1 3 = A x + B x 2 + 1 + C x + D x 2 + 1 2 + E x + F x 2 + 1 3 i.e. x 4 + 24 x 2 + 28 = A x + B x 2 + 1 2 + C x + D x 2 + 1 + E x + F x 4 + 24 x 2 + 28 = A x 5 + 2 A x 3 + A x + B x 4 + 2 B x 2 + B + C x 3 + D x 2 + C x + D + E x + F x 4 + 24 x 2 + 28 = A x 5 + B x 4 + 2 A + C x 3 + 2 B + D x 2 + A + C + E x + B + D + F i.e. A = 0 ,   B = 1 ,   2 A + C = 0 ,   2 B + D = 24 ,   A + C + E = 0 ,   B + D + F = 28 ⇒ A = 0 ,   B = 1 ,   C = 0 ,