Question

Rezolvati in multimea nr reale ecuatia: (3x+2)la a doua = 4
Nu-mi aduc aminte la ora asta , are formula (a+b) la a doua ?

Answer 1

$\it (3x+2)^2 =4 \Leftrightarrow (3x+2)^2 - 4 = 0 \Leftrightarrow (3x+2)^2 - 2^2 = 0$

$\it \Leftrightarrow (3x+2-2)(3x+2+2)=0 \Leftrightarrow 3x(3x+4) = 0 \Leftrightarrow$

$\it 3x+4=0 \Leftrightarrow x =-\dfrac{4}{3}$

$\it 3x =0 \Leftrightarrow x =0$

Ecuația admite două soluții : x = - 4/3  și  x = 0.

Answer 2

Ai doua metode : aplici (a+b)²=a²+2ab+b²

(3x+2)²=4
9x²+12x+4=4
9x²+12x=4-4
9x²+12x=0
3x(3x+4)=0
x₁=0; x₂= - 4/3

Sau aplici  a²-b²= (a+b)(a-b):

(3x+2)²=4
(3x+2)²- 4=0
(3x+2+2)(3x+2-2)=0
(3x+4)*3x=0
x₁=0
x₂= - 4/3

Cu ocazia aceasta iti aduci aminte de formule! :)