Given:

Using partial differentiation:

⇒ 1 = Ax² +Ax+ B+Bx+ Cx²

⇒ 1 = B + (A+B)x + (A+C)x²

Equating the coefficients of x, x² and constant value. We get:

(a) B = 1

(b) A + B = 0 ⇒ A = -B ⇒ A = -1

( c) A + C =0 ⇒ C = -A ⇒ C = 1

Put these values in equation (1)

⇒ L.H.S = R.H.S

Hence proved.