Evaluate- x2 -x -1 x-1 x-1 x-1

x^2 x +1 amp; x 1 x+1 amp; x+1=(x^2 x +1)(x+1) (x 1)(x+1)=x^3+1 (x^2 1)=x^3 x^2+2 ...

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Byju's Answer

Standard XII

Mathematics

Determinant

Evaluate: x2...

Question

Evaluate:
$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

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Solution

$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣ = (x^{2} - x + 1) (x + 1) - (x - 1) (x + 1) = x^{3} + 1 - (x^{2} - 1) = x^{3} - x^{2} + 2$

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Evaluate:∣∣∣x2−x+1x−1x+1x+1∣∣∣

∣∣∣x2−x+1x−1x+1x+1∣∣∣=(x2−x+1)(x+1)−(x−1)(x+1)=x3+1−(x2−1)=x3−x2+2

Evaluate:
$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣ = (x^{2} - x + 1) (x + 1) - (x - 1) (x + 1) = x^{3} + 1 - (x^{2} - 1) = x^{3} - x^{2} + 2$