Question Number 11 by user1 last updated on 25/Jan/15
$$\mathrm{Evaluate}:\:\: \\ $$$$\:\begin{vmatrix}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}&{{x}−\mathrm{1}}\\{\:\:\:\:\:{x}+\mathrm{1}}&{{x}+\mathrm{1}}\end{vmatrix} \\ $$
Answered by user1 last updated on 30/Oct/14
![=[(x^2 −x+1)(x+1)−(x+1)(x−1)] =[(x^3 +1)−(x^2 −1)] =(x^3 −x^2 +2)](https://www.tinkutara.com/question/Q12.png)
$$=\left[\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left({x}+\mathrm{1}\right)−\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)\right] \\ $$$$=\left[\left({x}^{\mathrm{3}} +\mathrm{1}\right)−\left({x}^{\mathrm{2}} −\mathrm{1}\right)\right] \\ $$$$=\left({x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}\right) \\ $$