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The complete solution set of the equatio...

The complete solution set of the equation `|x^2-5x+6|+|x^2+12x+27|=17x + 21 | ` is

A

`x in [-9,3]`

B

`x in [-3,2) cup (2,3] `

C

`x in [-9 , -3] cup [ 2,3]`

D

`x in (-2,3)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have `|x^2-5x+6|+|x^2+12x+27|=|17x+ 21|`
or `|x^2-5x+6|+|x^2+12x+27|`
`=|x^2+12x+27)-(x^2-5x+6)|`
`rArr (x^2-5x+6)(x^2+12x+27)le 0 `
`rArr (x-2)(x-3)(x+3)(x+9)le 0 `

From the sing scheme , `x in [-9,-3] cup [2,3]`
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