Question

Rezolvati in R ×R sistemul x+y=2
Xy=1

Answer 1

$\Big\{x+y = 2 \quad si \quad xy = 1 \Big\} \\ \\ Consideram: t^2-St+P = 0 \Rightarrow t^2-(x+y)t + xy = 0 \Rightarrow \\ \Rightarrow t^2-2t+1 = 0 \Rightarrow (t-1)^2 = 0 \Rightarrow t_1 = 1,\quad t_2 = 1 \\ \\ \Rightarrow \boxed{(x,y) = (1,1)}$