1) [tex] x^{2} -5x=0[/tex], Metoda I : x(x-5)=0 ⇒ [tex] x_{1}=0,si, x_{2}=5,deci: x_{1}^2+ x_{2}^2=25. [/tex]. Metoda a II-a, stim ca [tex]S= x_{1}+ x_{2}= \frac{-b}{a}=5,si,P= x_{1} x_{2}= \frac{c}{a}=0,iar, x_{1}^2 + x_{2}^2=S^2-2P [/tex]=25.
2) a doua ecuatie facand calculele (inmultind si cu -1) se obtine: [tex]3x^2-15x+10=0[/tex], radacinile sunt irationale deci aplicam metoda a II-a:
[tex] S= \frac{-b}{a} =5,siP= \frac{10}{3},deci: x_{1}^2+ x_{2}^2=S^2-2P=25- \frac{20}{3}= \frac{55}{3} [/tex]
