[tex] \frac{1}{x_1} + \frac{1}{x_2} = \frac{x_1 + x_2 }{x_1 x_2} = \frac{S_1}{S_2} [/tex]
Din relatiile lui Viete
[tex]S_1 = \frac{-b}{a} = \frac{3}{2}[/tex]
[tex]S_2 = \frac{c}{a} = 3[/tex]
[tex]\frac{1}{x_1} + \frac{1}{x_2} = \frac{3/2}{3} = 1/2[/tex]
b)
[tex] \frac{1}{x_1+3} + \frac{1}{x_2+3} = \frac{x_1 + x_2 + 6}{(x_1+3)(x_2+3)} =\frac{x_1 + x_2 + 6}{x_1x_2 + 3(x_1+x_2) + 9} = \frac{S_1+6}{S_2 + 3S_1 + 9} = \frac{3/2 + 6}{ 3 + 3* 3/2 + 9}[/tex]
[tex]\frac{3/2 + 6}{ 3 + 3* 3/2 + 9} = \frac{3 + 12}{3 + 9 + 18} = \frac{15}{30} =1/2[/tex]
