Question

Multimea solutiilor ecuatiei 4x^2-12x+8=0 este egala cu S = { ... }

Answer 1

$4x^2-12x+8=0$
Impartim la 4 sa avem calcule mai usoare

$x^2-3x+2=0$

Calculam delta

$D=9-8=1$

$x_1= \frac{3+ \sqrt{D} }{2}= \frac{3+1}{2}=2 \\ x_2= \frac{3- \sqrt{D}}{2}= \frac{3-1}{2}=1 \\ S=\{1,2\}$

Ecuatia de gradul 2 se rezolva astfel:
$ax^2+bx+c=0 \\ D= b^2-4ac \\ x_1= \frac{-b- \sqrt{D} }{2a} \\ x_2= \frac{-b+ \sqrt{D} }{2a}$

Answer 2

$4x^2-12x+8=0 \\ a=4,b=-12,c=8 \\ delta=b^2-4ac=12^2-4*4*8=144-128=16\ \textgreater \ 0 \\ x_1= \frac{12+ \sqrt{16} }{2*4} = \frac{12+4}{8} = \frac{16}{8} =2 \\ x_2= \frac{12- \sqrt{16} }{2*4} = \frac{12-4}{8} = \frac{8}{8} =1 \\ S= \left \{1;2 \left \}$