Răspuns:
a)[tex]\frac{-3}{2}[/tex]
b)[tex]\frac{-4}{5}[/tex]
Explicație pas cu pas:
[tex]4x^{2} +4x+5=0[/tex]
Folosim relatiile lui Viete:
[tex]S=x_{1} +x_{2} =\frac{-b}{a}[/tex]
[tex]P=x_{1} *x_{2} =\frac{c}{a}[/tex]
In cazul nostru:
- [tex]S=\frac{-4}{4} =-1[/tex]
a) [tex]x_1^{2} +x_2^{2} =(x_{1} +x_{2} )^2-2x_{1} x_{2} =S^2-2P=(-1)^2-\frac{2*5}{4} =1-\frac{5}{2} =\frac{2-5}{2} =\frac{-3}{2}[/tex]
b) [tex]\frac{1}{x_{1} } +\frac{1}{x_{2} } =\frac{x_{1}+x_{2} }{x_{1}*x_{2} } =\frac{S}{P} =\frac{-1}{\frac{5}{4} } =\frac{-4}{5}[/tex]
