Mathematics

Match the following with I, II, III 
If $$\displaystyle \frac{x^{2}-x+3}{x^{3}-1}=\frac{A}{(x-1)}+\frac{Bx+C}{(x^{2}+x+1)}$$ then

I) $$A=$$             a)  0
II) $$B=$$            b)  1
III) $$C=$$          c)  -2


ANSWER

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
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