X2-x-1-x-1x-2x-3-A-x-1-B-x-2-C-x-3 - A-C-

The correct option is D 8 x^2+x+1/(x 1)(x 2)(x 3)=A/x 1+B/x 2+C/x 3 ⇒ x^2+x+1=A(x 2)(x 3)+B(x 1)(x 3)+C(x 1)(x 2) , Cross multiply #160;Substitute ...

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Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

x2+x+1/x-1x-2...

Question

$\frac{x^{2} + x + 1}{(x - 1) (x - 2) (x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$
$\Rightarrow A + C =$

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Solution

The correct option is D 8
$\frac{x^{2} + x + 1}{(x - 1) (x - 2) (x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$
$\Rightarrow x^{2} + x + 1 = A (x - 2) (x - 3) + B (x - 1) (x - 3) + C (x - 1) (x - 2)$ , Cross multiply
Substitute $x = 1 \Rightarrow A = \frac{3}{2}$
Now substitute $x = 3 \Rightarrow C = \frac{13}{2}$
Hence $A + C = 8$

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Similar questions

Q. If

\frac{x^{2} + 5 x + 1}{(x + 1) (x + 2) (x + 3)} = \frac{A}{x + 1} + \frac{B}{(x + 1) (x + 2)} + \frac{C}{(x + 1) (x + 2) (x + 3)}

, then C=

Q. If

\frac{x^{2} + 5 x + 1}{(x + 1) (x + 2) (x + 3)} = \frac{A}{x + 1} + \frac{B}{(x + 1) (x + 2)}

+ \frac{C}{(x + 1) (x + 2) (x + 3)},

then

B

is equal to

\frac{x^{2} + 3 x + 5}{(x + 1) (x + 2) (x + 3)} =

\frac{A}{(x + 1)} + \frac{B}{(x + 1) (x + 2)} + \frac{c}{(x + 1) (x + 2) (x + 3)}

then ascending order of A, B, C is

Q. If

\frac{x^{3}}{(2 x - 1) (x + 2) (x - 3)} =

A + \frac{B}{(2 x - 1)} + \frac{C}{(x + 2)} + \frac{D}{(x - 3)}

then

A =

\frac{1}{(x - 1) (x + 2) (2 + 3)} = \frac{A}{x - 1} + \frac{B}{x + 2} + \frac{C}{2 x + 3}

. Match the variables with their values.

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x2+x+1(x−1)(x−2)(x−3)=Ax−1+Bx−2+Cx−3⇒A+C=

The correct option is D 8x2+x+1(x−1)(x−2)(x−3)=Ax−1+Bx−2+Cx−3⇒x2+x+1=A(x−2)(x−3)+B(x−1)(x−3)+C(x−1)(x−2), Cross multiply Substitute x=1⇒A=32Now substitute x=3⇒C=132Hence A+C=8

$\frac{x^{2} + x + 1}{(x - 1) (x - 2) (x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$
$\Rightarrow A + C =$