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Question Number 87556 by M±th+et£s last updated on 05/Apr/20

Commented by jagoll last updated on 05/Apr/20

$${\mathrm{x}}^3-{2\mathrm{x}}^2+7\mathrm{x}-1=\mathrm{a}{(\mathrm{x}-2)}^2+$$$$\mathrm{b}(\mathrm{x}-3){(\mathrm{x}-2)}^2+\mathrm{c}{(\mathrm{x}-3)}^2{(\mathrm{x}-2)}^2+$$$$\mathrm{d}{(\mathrm{x}-3)}^3+\mathrm{e}{(\mathrm{x}-3)}^3(\mathrm{x}-2)$$

Answered by $@ty@m123 last updated on 05/Apr/20

$$Let\frac{x^3-2x^2+7x-1}{{(x-3)}^3{(x-2)}^2}=\frac{A}{{(x-3)}^3}+\frac{B}{{(x-3)}^2}$$$$+\frac{C}{(x-3)}+\frac{D}{{(x-2)}^2}+\frac{E}{x-2}$$$$\Rightarrow A{(x-2)}^2+B(x-3){(x-2)}^2+C{(x-3)}^2{(x-2)}^2$$$$+D{(x-3)}^2+E{(x-3)}^3(x-2)=$$$$x^3-2x^2+7x-1....\left(i\right)$$$$Putx=0in\left(i\right)$$$$\Rightarrow 4A+12B+36C+9D+54E=-1...\left(ii\right)$$$$Putx=1in\left(i\right)$$$$A-2B+4C+4D-8E=5....\left(iii\right)$$$$Putx=2in\left(i\right)$$$$D=8-8+14-1=13$$$$Putx=3in\left(i\right)$$$$A=27-18+20=29$$$$Nowdoityourself:$$$$◼PutvaluesofA\mathrm{\&}Din\left(ii\right)\mathrm{\&}\left(iii\right)$$$$andformequation\left(iv\right)\mathrm{\&}\left(v\right)$$$$◼Putx=4in\left(i\right)andformequation\left(vi\right)$$$$◼Solve\left(iv\right),\left(v\right)\mathrm{\&}\left(vi\right)forB,C\mathrm{\&}Eusing$$$${Cramer}^{\prime }sRule.$$

Commented by peter frank last updated on 05/Apr/20

$$thankyou$$

Commented by M±th+et£s last updated on 05/Apr/20

$$godblessyousir$$

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