√x - 1 - x = - 7, este ecuatie irationala
√x - 1 = x - 7
1) C.E. = CONDITII DE EXISTENTA
X - 1 ≥ 0⇔ X ≥ 1 ⇒ X ∈ [ 1 , + 00)
X - 7 ≥ 0 ⇔ X ≥ 7 ⇒ X ∈ [ 7 , + 00)
X ∈ [ 7 , + 00), DOMENIUL DE DEFINITIE
2) REZOLVAREA ECUATIEI:
√X - 1 = X - 7, se ridica la puterea a doua
( √x - 1)² = ( x - 7)²
( x - 7)² = x - 1
x² - 12x + 49 = x - 1
x² - 12x + 49 - x + 1 = 0
x² - 13x + 50 = 0, ecuatie de gradul II
a = 1, b = - 13, c = 50
delta = b² - 4ac = ( - 13)² - 4·1·50 = 169 - 200 = - 31
delta = - 13 ⇒ delta , 0, ecuatia nu are solutii reale
S = Ф, MULTIMEA VIDA
