Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 582

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

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

\[D = 9 - 8 = 1\]

\[x_{1} = \frac{3 + 1}{2} = 2;\ \ \]

\[x_{2} = \frac{3 - 1}{2} = 1.\]

\[(x - 1)(x - 2) \geq 0\]

\[x \leq 1;\ \ \ x \geq 2.\]

\[2)\ y = \sqrt{x^{2} + 5x - 6}\]

\[x^{2} + 5x - 6 \geq 0\]

\[x_{1} + x_{2} = - 5;\ \ x_{1} \cdot x_{2} = - 6\]

\[x_{1} = - 6;\ \ \ x_{2} = 1.\]

\[(x + 6)(x - 1) \geq 0\]

\[x \leq - 6;\ \ x \geq 1.\]

\[3)\ y = \frac{1}{x^{2} + 7x - 8}\]

\[x^{2} + 7x - 8 \neq 0\]

\[x_{1} + x_{2} = - 7;\ \ x_{1} \cdot x_{2} = - 8\]

\[x_{1} \neq - 8;\ \ \ x_{2} \neq 1.\]

\[4)\ y = \frac{2}{2x^{2} + 7x - 4}\]

\[2x^{2} + 7x - 4 \neq 0\]

\[D = 49 + 32 = 81\]

\[x_{1} \neq \frac{1}{2};\ \ \ x_{2} \neq - 4.\]