If (x+1)² x³+x = A x + B x+C x²+1 , then ⁻¹ A+ ⁻¹ B+ ⁻¹ C is equal to

Step-by-step solution

Given, (x+1)² x³+x = A x + B x+C x²+1 ...(i) aligned (x+1)² &=A (x²+1 )+(B x+c)(x) x²+1+2 x &=A x²+A+B x²+C x &=(A+B) x²+C x+A aligned On comparing the coefficient of like powers on both sides, we get A+B=1...(ii) and C=2, A=1 From Eq. (ii), B=0 Then, ⁻¹ A+ ⁻¹ B+ ⁻¹ C= ⁻¹(1)+ ⁻¹(0)+ ⁻¹(2)= ⁻¹ 2 + ⁻¹ 0+ ⁻¹ 3 = 2 +0+ 3 = 5 6