ГДЗ по алгебре 8 класс Макарычев Задание 548

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Год:2021
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Задание 548

\[\boxed{\text{548\ (549).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ x^{2} - 2x - 1 = 0\]

\[x^{2} = 2x + 1\]

\[\left\{ \begin{matrix} y = x^{2}\text{\ \ \ \ \ \ \ \ } \\ y = 2x + 1 \\ \end{matrix} \right.\ \]

\[y = x^{2}\]

\[x\] \[0\] \[1\] \[2\] \[- 1\] \[- 2\]
\[y\] \[0\] \[1\] \[4\] \[1\] \[4\]

\[y = 2x + 1\]

\[x\] \[0\] \[1\]
\[y\] \[1\] \[3\]

\[x^{2} - 2x - 1 = 0\]

\[D = 4 + 4 = 8\]

\[x_{1} = \frac{2 - \sqrt{8}}{2} = \frac{2 - 2\sqrt{2}}{2} = - 0,4;\]

\[x_{2} = \frac{2 + \sqrt{8}}{2} = \frac{2 + 2\sqrt{2}}{2} = 2,4.\]

\[Ответ:x = - 0,4;\ \ x = 2,4.\ \]

\[\textbf{б)}\ x^{2} - 4x + 2 = 0\]

\[x^{2} = 4x - 2\]

\[\left\{ \begin{matrix} y = x^{2} \\ y = 4x - 2 \\ \end{matrix} \right.\ \]

\[y = x^{2}\]

\[x\] \[0\] \[1\] \[2\] \[- 1\] \[- 2\]
\[y\] \[0\] \[1\] \[4\] \[1\] \[4\]

\[y = 4x - 2\]

\[x\] \[0\] \[1\]
\[y\] \[- 2\] \[2\]

\[x^{2} - 4x + 2 = 0\]

\[D = 16 - 8 = 8\]

\[x_{1} = \frac{4 - \sqrt{8}}{2} = \frac{4 - 2\sqrt{2}}{2} = 0,6;\]

\[x_{2} = \frac{4 + \sqrt{8}}{2} = \frac{4 + 2\sqrt{2}}{2} = 3,4.\]

\(\ \)

\[Ответ:x = 3,4;\ \ x = 0,6.\]

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