A) \[-2,\text{ }2,\text{ }4\]
B) \[-2,\text{ }2,-4\]
C) 4, 3, 3
D) \[3,\text{ }2,-2\]
Correct Answer: A
Solution :
\[|{{x}^{2}}-x-6|=x+2\] or \[{{x}^{2}}-x-6=\pm (x+2)\] On taking \['+'\]sign, \[{{x}^{2}}-x-6=x+2\] \[\Rightarrow \] \[{{x}^{2}}-2x-8=0\] \[\Rightarrow \] \[(x-4)(x+2)=0\] \[\Rightarrow \] \[x=4,-2\] On taking\['-'\]sign \[{{x}^{2}}-x-6=-(x+2)\] \[\Rightarrow \] \[{{x}^{2}}-4=0\] \[\Rightarrow \] \[(x-2)(x+2)=0\] \[\Rightarrow \] \[x=2,-2\] Hence, solutions of given equations are\[-2,2,4\].
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