The value of x2-10x-3-x-1x-2x-3 is-

The correct option is B 13/x 2 9/x 3 3/x 1 x^2 10x+3/(x 1)(x 2)(x 3)=A/x 1+B/x 2+C/x 3 ⇒ nbsp;x^2 10x+3=A(x^2 5x+6)+B(x^2 4x+3)+C(x^2 3x+2) ...

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Standard XII

Mathematics

Chain Rule of Differentiation

The value of ...

Question

The value of $\frac{x^{2} - 10 x + 3}{(x - 1) (x - 2) (x - 3)}$ is:

\frac{3}{x - 2} + \frac{9}{x - 3} + \frac{10}{x - 1}

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\frac{13}{x - 2} - \frac{9}{x - 3} - \frac{3}{x - 1}

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\frac{9}{x - 3} + \frac{13}{x - 2} + \frac{3}{x - 1}

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\frac{9}{x - 2} + \frac{13}{x - 3} + \frac{3}{x - 1}

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Solution

The correct option is B $\frac{13}{x - 2} - \frac{9}{x - 3} - \frac{3}{x - 1}$
$\frac{x^{2} - 10 x + 3}{(x - 1) (x - 2) (x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3}$
$\Rightarrow x^{2} - 10 x + 3 = A (x^{2} - 5 x + 6) + B (x^{2} - 4 x + 3) + C (x^{2} - 3 x + 2)$
$\Rightarrow A + B + C = 1$
$- 5 A - 4 B - 3 C = - 10$
$6 A + 3 B + 2 C = 3$
On solving, we get $A = - 3, B = 13, C = - 9$
$\frac{x^{2} - 10 x + 3}{(x - 1) (x - 2) (x - 3)} = \frac{- 3}{x - 1} + \frac{13}{x - 2} + \frac{- 9}{x - 3}$

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The value of x2−10x+3(x−1)(x−2)(x−3) is:

The correct option is B 13x−2−9x−3−3x−1x2−10x+3(x−1)(x−2)(x−3)=Ax−1+Bx−2+Cx−3⇒x2−10x+3=A(x2−5x+6)+B(x2−4x+3)+C(x2−3x+2)⇒A+B+C=1 −5A−4B−3C=−10 6A+3B+2C=3On solving, we get A=−3,B=13,C=−9x2−10x+3(x−1)(x−2)(x−3)=−3x−1+13x−2+−9x−3

The value of $\frac{x^{2} - 10 x + 3}{(x - 1) (x - 2) (x - 3)}$ is: