Question

Daca x1, x2 sunt radacinile ecuatiei x**2-2x+3=0 si S=x1**2+x**2 atunci S=?

Answer 1

$\hbox{ Relatiile lui Viete} \longrightarrow\left \{ {{x_1+x_2= -\frac{b}{a} } \\ \atop {\\ x_1*x_2=\frac{c}{a}}}} \right. \\\\\\ x_1+x_2=-\frac{-2}{1} \to 2 \\\\ x_1*x_2= \frac{3}{1} \to 3 \\\\\\ (x_1+x_2)^2-2x_1x_2=x_1^2+x^2_2 \\\\ (x_1+x_2)^2-2x_1x_2=S \\\\ 2^2-2*3=S \\\\S=4-6\\\\\ \boxed{S=-2}$

Answer 2

Formulele lui Viète :

[tex]\it x_1+x_2 = -\dfrac{b}{a} =-\dfrac{-2}{1} =2 [/tex]

$\it x_1x_2=\dfrac{c}{a} =\dfrac{3}{1}=3$

$\it x_1^2 +x_2^2 = (x_1+x_2)^2 - 2x_1x_2 = 2^2- 2\cdot3 = 4 - 6 =-2$