ГДЗ по алгебре 8 класс Мерзляк Задание 782

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\[1)\ x - 6\sqrt{x} + 8 = 0\]

\[\left\{ \begin{matrix} \sqrt{x} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t^{2} - 6t + 8 = 0 \\ \end{matrix} \right.\ \text{\ \ }\]

\[t_{1} + t_{2} = 6,\ \ t_{1} \cdot t_{2} = 8,\ \]

\[\ t_{1} = 4,\ \ t_{2} = 2\]

\[Ответ:x = 16;x = 4.\]

\[2)\ x - 5\sqrt{x} - 50 = 0\]

\[\left\{ \begin{matrix} \sqrt{x} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ t^{2} - 5t - 50 = 0 \\ \end{matrix} \right.\ \]

\[t_{1} + t_{2} = 5,\ \ t_{1} \cdot t_{2} = - 50,\ \ \]

\[t_{1} = 10,\ \ t_{2} = - 5\]

\[\left\{ \begin{matrix} \sqrt{x} = t \\ t = 10 \\ t = - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} \sqrt{x} = 10 \\ \sqrt{x} = - 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[x = 100\]

\[Ответ:x = 100.\]

\[3)\ 2x - 3\sqrt{x} + 1 = 0\]

\[\left\{ \begin{matrix} \sqrt{x} = t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2t^{2} - 3t + 1 = 0 \\ \end{matrix} \right.\ \text{\ \ }\]

\[D = 9 - 8 = 1\]

\[\text{\ \ }t_{1,2} = \frac{3 \pm 1}{4}\]

\[Ответ:x = 1;x = \frac{1}{4}.\]