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Question Number 49123 by Pk1167156@gmail.com last updated on 03/Dec/18

$$\mathrm{If}$$$${\mathrm{a}}^3-\mathrm{a}-1=0$$$$\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{valueof}$$$${\mathrm{a}}^4+{\mathrm{a}}^3-{\mathrm{a}}^2-2\mathrm{a}+1$$

Commented by behi83417@gmail.com last updated on 03/Dec/18

$$a^3=a+1$$$$=a^3(a+1)-{(a+1)}^2+2=a^3\left(a^3\right)-{\left(a^3\right)}^2+2=2.$$

Answered by mr W last updated on 03/Dec/18

$$a^3=a+1$$$${\mathrm{a}}^4+{\mathrm{a}}^3-{\mathrm{a}}^2-2\mathrm{a}+1$$$$=a(a+1)+{\mathrm{a}}^3-{\mathrm{a}}^2-2\mathrm{a}+1$$$$={\mathrm{a}}^3-\mathrm{a}+1$$$$={\mathrm{a}}^3-\mathrm{a}-1+2$$$$=0+2$$$$=2$$

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