Question

Resolve
4x- 7x² + 5x - 4/
(x²-1)(x² – 3x+2)
into partial fractions​

Answer 1

Answer:

Correct option is

C

x

2

+1

x

+

x−2

2

+

x−1

1

Let

(x

2

+1)(x

2

−3x+2)

4x

3

−7x

2

+5x−4

=

x

2

+1

Ax+B

+

x−2

C

+

x−1

D

⇒4x

3

−7x

2

+5x−4=(Ax+B)(x−2)(x−1)+C(x

2

+1)(x−1)+D(x

2

+1)(x−2)

⇒4x

3

−7x

2

+5x−4=A(x

3

−3x

2

+2x)+B(x

2

−3x+2)+C(x

3

−x

2

−x−1)+D(x

3

−2x

2

+x−2)

On comparing coefficients we get

A+C+D=4,−3A+B−C−2D=−7,2A−3B−C+D=5,2B−C−2D=−4

⇒A=1,B=0,C=2,D=1

Hence

(x

2

+1)(x

2

−3x+2)

4x

3

−7x

2

+5x−4

=

x

2

+1

x

+

x−2

2

+

x−1

1

Hence, option 'C' is correct.

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