III) 2) Determinati multimea:
A = {x| x∈ℝ, |2x=4| = 6 }
Rezolvare:
Avem de rezolvat ecuatia |2x - 4| = 6.
Procedam astfel:
|2x - 4| = 6 ⇔ 2x - 4 = ± 6
Avem 2 cazuri:
I) 2x - 4 = -6 ⇔ 2x = -6 + 4 ⇔ 2x = -2 ⇔x = -2:2 ⇔ x = -1
II) 2x - 4 = 6 ⇔ 2x = 6 + 4 ⇔ 2x = 10 ⇔ x = 5
Ecuatia din enunt are 2 solutii x = -1, x= = 5.
Deci : A = {-1, 5}
Observatie:
Am folosit formula: |a| = b ⇔ a = ± b
