Mathematics

# Match the following with I, II, III If $\displaystyle \frac{x^{2}-x+3}{x^{3}-1}=\frac{A}{(x-1)}+\frac{Bx+C}{(x^{2}+x+1)}$ thenI) $A=$             a)  0II) $B=$            b)  1III) $C=$          c)  -2

b, a, c

##### SOLUTION
$\frac{x^{2}-x+3}{x^{3}-1}=\frac{A(x^{2}+x+1)+(Bx+C)(x-1)}{(x-1)(x^{2}+x+1)}$
equating the co-efficients we get
$A+B=1$
$A-B+C=-1$
$A-C=3$
Solving we get  $A=1; B=0; C=-2$
So, $A \equiv b; B \equiv a; C \equiv c$
b,a,c

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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1 Verified Answer | Published on 17th 09, 2020

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