Question

Ma ajuta cineva ? Va rog
Rezolvați in R ec
1) 3x²-2x+1=0
2) -4x²+9x-2=0
3) 4x²-2x-3=0
4) 9x²-12x+4=0
5) -7x²-3x-10=0

Answer 1

Răspuns:

pentru a rezolva ecuatiile de gradul 2 aplicam formula

x₁ ₂ = [- b ± √(b² - 4ac)]/2a

3x² - 2x + 1 = 0

a = 3 ; b = -2 ; c = 1

x₁ ₂ = (2 ± √(4 - 4·3·1)/2·3

= (2 ± √(4 - 12)/6

= (2 ± √-8)/5

x ∉ R deoarece avem √-8

-4x² + 9x - 2 = 0

4x² - 9x + 2 = 0

a = 4 ; b = - 9 ; c = 2

x₁ ₂ = (9 ± √(-9)² - 4·4·2)/2·4

= (9 ± √49)/8

= (9 ± 7)/8

x₁ = (9+7)/8 = 16/8 = 2

x₂ = (9-7)/8 = 2/8 = 1/4

4x² - 2x - 3 = 0

a = 4 ; b = -2 ; c = -3

x₁ ₂ = (2 ± √4+48)/8

= (2 ± √52)/8

= (2 ± 2√13)/8

= 2(1 ± √13)/8

= (1 ± √13)/4

x₁ = (1 + √13)/4

x₂ = (1 - √13)/4

ti-am facut 3 exemple, cu celelalte 2 exersezi singur