Question

|X^2 - X - 6| = x + 2. value of x ​

Answer 1

Answer:

∣x

2

−x−6∣=x+2, then

Case I: x

2

−x−6<0

⇒(x−3)(x+2)<0

⇒−2<x<3

In this case, the equation becomes

x

2

−x−6=−x−2

or x

2

−4=0

∴x=±2

Clearly, x=2 satisfies the domain of the equation in this case. So, x=2 is a solution.

Case II: x

2

−x−6≥0

So, x≤−2 or x≥3

In this case, the equation becomes

x

2

−x−6=0=x+2

i.e., x

2

−2x−8=0 or x=−2,4

Both these values lie in the domain of the equation in this case, so x=−2,4 are the roots.

Hence, roots are x=−2,2,4