Question

scrieti o ecuatie cu gradul 2cu multimea solutiilor S={1-/3;1+/3

Answer 1

   
[tex]\displaystyle \\ \text{Calculam suma si produsul radacinilor: }\\ S=(1-\sqrt{3})+(1+\sqrt{3})=1+1-\sqrt{3}+\sqrt{3}=\boxed{2}\\ P=(1-\sqrt{3})\times (1+\sqrt{3})=1^2-(\sqrt{3})^2=1-3=\boxed{-2}\\ \text{Fcuatia este: } \\ x^2-Sx+ P = 0\\ \boxed{x^2-2x-2=0}\\ Verificare:\\ x_{12} = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{2 \pm \sqrt{4 + 8} }{2} = \frac{2 \pm \sqrt{12} }{2} =1\pm \sqrt{3}[/tex]