c)
[tex]x_{1} = 1- \sqrt{2}[/tex]
[tex]x_{2} = 1 + \sqrt{2}[/tex]
[tex]S = 1 - \sqrt{2} + 1 + \sqrt{2} \Rightarrow S = 2[/tex]
[tex]P = (1-\sqrt{2} ) (1+\sqrt{2} ) = P = 1^2-(\sqrt{2} )^2 = 1-2 = -1[/tex]
[tex]\Rightarrow \boxed{x^2-2x-1=0}[/tex]
b)
[tex]x_{1} = 3(\frac{1}{2} )= \frac{3}{2}[/tex]
[tex]x_{2} = 2\2(\frac{1}{2} )= \frac{3}{5} = -\frac{6}{5}[/tex]
[tex]S = \frac{3}{2} -\frac{6}{5} =\frac{15-12}{10} = \frac{3}{10}[/tex]
[tex]P = \frac{3}{2} \cdot (-\frac{6}{5} ) = -\frac{9}{5}[/tex]
[tex]\Rightarrow x^{2} -\frac{3x}{10} - \frac{9}{x} = 0 \Rightarrow \boxed{x^2-2x-1=0}[/tex]
Sper ca te-am ajutat!
