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The roots of the equation \(\left|x^2-x-6\right|=x+2\) are
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Verified Answer
The correct answer is:
\(-2,2,4\)
Given, \(\left|x^2-x-6\right|=x+2\)
\(\begin{array}{ll}
\Rightarrow & x^2-x-6=x+2 \\
\text {Or } & x^2-x-6=-x-2 \\
\Rightarrow & x^2-2 x-8=0 \text { or } x^2=4 \\
\Rightarrow & (x=-2,4) \text { or }(x= \pm 2) \Rightarrow x=\{-2,2,4\}
\end{array}\)
\(\begin{array}{ll}
\Rightarrow & x^2-x-6=x+2 \\
\text {Or } & x^2-x-6=-x-2 \\
\Rightarrow & x^2-2 x-8=0 \text { or } x^2=4 \\
\Rightarrow & (x=-2,4) \text { or }(x= \pm 2) \Rightarrow x=\{-2,2,4\}
\end{array}\)
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