tentukan penyelesaian |4x+1|kuadrat-5|4x+1|+6=0

Matematika Wajib
Persamaan Mutlak X SMA

Pembahasan :
|4x + 1|² - 5|4x + 1| + 6 = 0

Misal |4x + 1| = a
a² - 5a + 6 = 0
(a - 3)(a - 2) = 0

a = 3
|4x + 1| = 3
(4x + 1)² = 3²
(4x + 1)² - 3² = 0
(4x + 1 + 3)(4x + 1 - 3) = 0
(4x + 4)(4x - 2) = 0
x = -1
x = 1/2

a = 2
|4x + 1| = 2
(4x + 1)² = 2²
(4x + 1)² - 2² = 0
(4x + 1)² - 2² = 0
(4x + 1 + 2)(4x + 1 - 2) = 0
(4x + 3)(4x - 1) = 0
x = -3/4
x = 1/4

Hp : {-1 , -3/4 , 1/4 , 1/2}