Question

rezolvati in r ecuatiile de gradul ||,forma incompleta a) 3x²-12=0. b) 2x²-5x=0 prin doua metode

Answer 1

a) Metoda 1
3x²-12=0⇒ 3(x²-4)=0⇒ 3(x-2)(x+2)=0⇒ x-2=0 sau x+2=0⇒ x=2 sau x=-2

Metoda 2
3x²-12=0
a=3; b=0; c=-12
Δ=b²-4ac
Δ= 4*12*3=144⇒√Δ=12
x₁,₂=(-b +/- √Δ) :2a
x=12/6=2 sau x=-12/6=-2
3(x-2)(x+2)=2

x∈{2,-2}

b)Metoda 1
 2x²-5x=0 ⇒ x(2x-5)=0⇒ x=0 sau 2x-5=0⇒2x=5⇒ x=5/2

Metoda 2
a=2, b=5, c=0
Δ=5²-4*2*0=25⇒√Δ=5
x=-5+5/4=0 sau x=-5-5/4=-10/4=-5/2
2x(x-5/2)=0

x∈{0 ; 5/2}