Решебник по алгебре 8 класс Мерзляк ФГОС Задание 1138

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\[1)\ \sqrt{x^{2} + 3x - 4} + \sqrt{x^{2} + 6x + 8} = 0\]

\[x^{2} + 3x - 4 = 0\]

\[x_{1} + x_{2} = - 3,\ \ x_{1}x_{2} = - 4,\ \]

\[\ x_{1} = - 4,\ \ x_{2} = 1\]

\[x^{2} + 6x + 8 = 0\]

\[x_{1} + x_{2} = - 6,\ \ x_{1}x_{2} = 8,\ \ \]

\[x_{1} = - 4,\ \ x_{2} = - 2\]

\[Ответ:\ x = - 4.\]

\[2)x² - 4x + 4 + \left| x^{2} - 3x + 2 \right| = 0\]

\[\ \left\{ \begin{matrix} x^{2} - 4x + 4 = 0 \\ x^{2} - 3x + 2 = 0 \\ \end{matrix} \right.\ \]

\[(x - 2)^{2} = 0\]

\[x = 2\]

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

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

\[x_{1} = 2,\ \ x_{2} = 1\]

\[Ответ:x = 2.\]

\[3)\ \sqrt{25 - x^{2}} + \left| x^{2} + 8x - 20 \right| = 0\]

\[25 - x^{2} = 0\]

\[x² = 25\]

\[x = 5,\ \ x = - 5\]

\[x^{2} + 8x - 20 = 0\]

\[x_{1} + x_{2} = - 8,\ \ x_{1}x_{2} = - 20,\ \ \]

\[x_{1} = - 10,\ \ x_{2} = 2\]

\[Ответ:нет\ корней.\]