Mathematics

If $$\displaystyle \frac{\mathrm{x}^{4}+1}{(\mathrm{x}-1)(\mathrm{x}-2)}=\mathrm{A}\mathrm{x}^{2}+\mathrm{B}\mathrm{x}+\mathrm{C}-\frac{2}{\mathrm{x}-1}+\frac{17}{\mathrm{x}-2}$$, then $$\mathrm{C}=$$


ANSWER

$$7$$


SOLUTION
In the equation
$$\displaystyle \frac{x^{4}+1}{(x-1)(x-2)}=Ax^{2}+Bx+C-\frac{2}{x-1}+\frac{17}{x-2}$$
put $$x=0$$
$$\dfrac{1}{2}=C+24-\dfrac{17}{2}$$
$$c=7$$
the value of $$c=7$$
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Single Correct Medium Published on 17th 09, 2020
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