Решебник по алгебре 9 класс Макарычев Задание 1047

\[\boxed{\text{1047\ (1047).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x^{2} - 3ax + a^{2} = 0,\]

\[x_{1}^{2} + x_{2}^{2} = 1,75;\]

\[x_{1} - ?\ \ \ \ x_{2} - ?\]

\[По\ теореме\ Виета:\]

\[x_{1} + x_{2} = 3a,\]

\[x_{1} \cdot x_{2} = a^{2},\]

\[\left( x_{1} \right)^{2} + \left( x_{2} \right)^{2} =\]

\[= \left( x_{1} + x_{2} \right)^{2} - 2x_{1}x_{2} = 1,75;\]

\[9a^{2} - 2a^{2} = 1,75;\]

\[7a^{2} = 1,75\]

\[a^{2} = 0,25 \Longrightarrow a = \pm 0,5.\]

\[4x_{1}^{2} - 6x_{1} + 1 = 0\]

\[D = 36 - 16 = 20 = 2\sqrt{5},\]

\[x_{1,2} = \frac{6 \pm 2\sqrt{5}}{8} = \frac{3 \pm \sqrt{5}}{4}\text{.\ }\]

\[4x_{1}^{2} + 6x_{1} + 1 = 0\]

\[D = 36 - 16 = 20 = 2\sqrt{5},\]

\[x_{1,2} = \frac{- 6 \pm 2\sqrt{5}}{8} = \frac{- 3 \pm \sqrt{5}}{4}\text{.\ }\]