Rozwiązanie:
Ze wzorów Viete'a wiadomo, że:
[tex]x_{1}+x_{2}=-\frac{b}{a}\\(x_{1}-x_{2})^{2}=(x_{1}+x_{2})^{2}-4x_{1}x_{2}=(\frac{b}{a} )^{2}-\frac{4c}{a} \\x_{1}-x_{2}=\sqrt{(\frac{b}{a} )^{2}-\frac{4c}{a}}[/tex]
Zatem:
a)
[tex]\Delta=81-4*1*(-7)>0\\x_{1}+x_{2}=9\\x_{1}-x_{2}=\sqrt{81+28}=\sqrt{109}[/tex]
b)
[tex]\Delta=9-4*(-2)*7>0\\x_{1}+x_{2}=\frac{3}{2}\\x_{1}-x_{2}=\sqrt{\frac{9}{4}+14 } =\sqrt{\frac{65}{4} } =\frac{\sqrt{65} }{2}[/tex]
