|x-3|^2-8|x-3|>-12 Tolong di jawab :)

Pertdksamaan NiLai MutLak

Misal :
|x - 3| = a

|x - 3|² - 8|x - 3| > -12
a² - 8a + 12 > 0
(a - 2)(a - 6) > 0
a < 2 atau a > 6

•
Utk a < 2
|x - 3| < 2
-2 < x - 3 < 2
-2 + 3 < x < 2 + 3
1 < x < 5 ... (1)

•
Utk a > 6
|x - 3| > 6
x - 3 > 6
x > 9 .. (2)

x - 3 < -6
x < -3 ... (3)

Nilai x yg memenuhi :
x < -3
x > 9
1 < x < 5

|x-3|^2-8|x-3|>-12
(x-3)^2-8(x-3)>-12
x^2-6x+9-8x+24>-12
x^2-14x+33>-12
x^2-14x+33+12>0
x^2-14x+45>0
(x-9)(x-5)>0
x-9>0 atau x-5<0
x>9 atau x<5

(x-3)^2+8(x-3)>-12
x^2-6x+9+8x-24>-12
x^2+2x-15>-12
x^2+2x-15+12>0
x^2+2x-3>0
(x+3)(x-1)>0
x+3<0 atau x-1>0
x<-3 atau x>1
Jadi HPnya adalah {x>9 , x<-3 , 1<x<5}