Let Now putting, A(x-1) 2 +B(x-3)(x-1)+C(x-3)=x 2 +1 Putting x-1=0, X=1 A(0)+B(0)+C(1-3)=1+1 C=-1 Putting x-3=0, X=3 A(3-1) 2 +B(0)+C(0)=9+1 A(4)=10 Equating the coefficient of x 2 A+B=1 From (i)

Evaluate:

Let

Now putting,

A(x-1)²+B(x-3)(x-1)+C(x-3)=x²+1

Putting x-1=0,

X=1

A(0)+B(0)+C(1-3)=1+1

C=-1

Putting x-3=0,

X=3

A(3-1)²+B(0)+C(0)=9+1

A(4)=10

Equating the coefficient of x²

A+B=1

From (i)