Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1328

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\[1)\ (x - 3)(x - 2) = 6(x - 3)\]

\[x^{2} - 2x - 3x + 6 = 6x - 18\]

\[x^{2} - 5x + 6 = 6x - 18\]

\[x^{2} - 11x + 24 = 0\]

\[D = 121 - 96 = 25\]

\[x_{1} = \frac{11 - 5}{2} = \frac{6}{2} = 3;\]

\[x_{2} = \frac{11 + 5}{2} = \frac{16}{2} = 8.\]

\[Ответ:\ \ 3;\ 8.\]

\[2)\ x^{2} - \frac{11x}{6} + \frac{1}{2} = 0\ \ \ \ \ |\ \bullet 6\]

\[6x^{2} - 11x + 3 = 0\]

\[D = 121 - 72 = 49\]

\[x_{1} = \frac{11 - 7}{2 \bullet 6} = \frac{4}{12} = \frac{1}{3};\]

\[x_{2} = \frac{11 + 7}{2 \bullet 6} = \frac{18}{12} = \frac{3}{2}.\]

\[Ответ:\ \ \frac{1}{3};\ \frac{3}{2}.\]