We have,x2−x−6=x+2⇒ x2−x−6=±(x+2)Taking positive sign, we getx2−x−6=(x+2)⇒x2−2x−8=0⇒(x−4)(x+2)=0⇒x=−2,4Taking negative sign, we getx2−x−6=−(x+2)⇒x2−4=0⇒x=2Hence the solution set is {-2, 2, 4}.

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$|x^{2} - x - 6| = x + 2$

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{-12, 2, 4}

{-2, 2, 14}

{-2,12, 4}

{-2, 2, 4}

answer is D.

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Detailed Solution

We have,

$\begin{array}{l} |x^{2} - x - 6| = x + 2 \\ \Rightarrow (x^{2} - x - 6) = \pm (x + 2) \end{array}$

Taking positive sign, we get

$\begin{array}{l} (x^{2} - x - 6) = (x + 2) \\ \Rightarrow (x^{2} - 2 x - 8) = 0 \\ \Rightarrow (x - 4) (x + 2) = 0 \\ \Rightarrow x = - 2, 4 \end{array}$