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If |x^2- 2x- 8| + |x^2+ x -2|= 3|x +2|,...

If `|x^2- 2x- 8| + |x^2+ x -2|= 3|x +2|`, then the set of all real values of `x` is

A

`[1,4] uu {-2}`

B

`[1,4]`

C

`[-2,1] uu [4,oo)`

D

`(-oo,-2] uu [1,4]`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `|x^(2)-2x-8|+|x^(2)+x-2|=3|x+2|`
Now `(x^(2)+x-2)-(x^(2)-2x-8)=3x+6=3(x+2)`
`:. (x^(2)-2x-8)(x^(2)+x-2) le 0`
`(x-4)(x+2)^(2)(x-1) le 0`
The sign scheme is shown below.

From the sign scheme, `x in [1,4]uu{-2}`
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