Какие из уравнений не имеют корней: x^2+9=0.

Ответ:

\[b + b^{2} = \frac{1 + 2b}{2} \Longrightarrow 2b + 2b^{2} =\]

\[= 1 + 2b \Longrightarrow 2b^{2} = 1 \Longrightarrow b^{2} =\]

\[= \frac{1}{2} \Longrightarrow b = \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{\sqrt{2}} \Longrightarrow\]

\[\Longrightarrow a_{1} = 1 + \frac{\sqrt{2}}{2} = \frac{2 + \sqrt{2}}{2}\ \ \ и\ \ \]

\[\ a_{2} = 1 - \frac{\sqrt{2}}{2} = \frac{2 - \sqrt{2}}{2}\]

\[Ответ:\ \ a = \frac{2 + \sqrt{2}}{2};\ \ b = \frac{\sqrt{2}}{2};\ \ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a = \frac{2 - \sqrt{2}}{2};\ \ \ b = - \frac{\sqrt{2}}{2}.\]