Question

Rezolvati in R ecuatiile:
a) x² + 10x=24
b) 25x²-10x-8=0
c) 3x² - 2√3x - 15=0

Answer 1

a) x²+10x -24=0
x²+12x-2x-24=0
x(x+12) -2(x+12)=0
(x+12)(x-2)=0⇒ x+12=0 ⇒ x=-12 sau x-2=0⇒ x=2
x∈ {-12;2}

b) 25x² -20x+10x -8=0
5x(5x-4) +2(5x-4)=0
(5x-4) (5x+2)=0 ⇒ 5x-4=0 ⇒ 5x=4⇒x=4/5 sau 5x+2=0 ⇒ x=-2/5
x∈ { 4/5 ; -2/5}

c) Δ = 12+180=192 ⇒ √Δ=8√3
x= (2√3+8√3)/6 = 10√3/6=5√3/3
x=(2√3-8√3)/6 = -6√3/6=-√3