|x-1|^2 - |x-1| =0 hasil nya brp ya?tlg bantu

Mapel : Matematika
Kelas : X SMA
Bab : Persamaan Nilai Mutlak

Pembahasan :
|x - 1|² - |x - 1| = 0

Misal |x - 1| = a
Maka...

a² - a = 0
a(a - 1) = 0

a = 0
|x - 1| = 0
x - 1 = 0
x = 1

a - 1 = 0
a = 1
|x - 1| = 1
(x - 1)² = 1²
(x - 1)² - 1² = 0
(x - 1 + 1)(x - 1 - 1) = 0
x(x - 2) = 0
x = 0 , x = 2

Hp : {0,1,2}