Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 153

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

\[2x + 3 = 1\]

\[2x = - 2\]

\[x = - 1\]

\[Ответ:\ \ x = - 1.\]

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

\[1 - x = 8\]

\[x = 1 - 8\]

\[x = - 7\]

\[Ответ:\ \ x = - 7.\]

\[3)\ \sqrt[3]{3x^{2} - 3} = \sqrt[3]{8x}\]

\[3x^{2} - 3 = 8x\]

\[3x^{2} - 8x - 3 = 0\]

\[D = 8^{2} + 4 \bullet 3 \bullet 3 =\]

\[= 64 + 36 = 100\]

\[x_{1} = \frac{8 - 10}{2 \bullet 3} = - \frac{2}{6} = - \frac{1}{3};\]

\[x_{2} = \frac{8 + 10}{2 \bullet 3} = \frac{18}{6} = 3.\]

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