Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1333

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\[{1)\ x^{4} - 11x^{2} + 30 = 0 }{y = x^{2}:}\]

\[y^{2} - 11x^{2} + 30 = 0\]

\[D = 121 - 120 = 1\]

\[y_{1} = \frac{11 - 1}{2} = 5;\ \]

\[y_{2} = \frac{11 + 1}{2} = 6;\]

\[x_{1} = \pm \sqrt{5};\ x_{2} = \pm \sqrt{6}.\]

\[Ответ:\ \ x_{1} = \pm \sqrt{5};\ \ x_{2} = \pm \sqrt{6}.\]

\[2)\ 2x^{4} - 5x^{2} + 2 = 0\]

\[y = x^{2}:\]

\[D = 25 - 16 = 9\]

\[y_{1} = \frac{5 - 3}{2 \bullet 2} = \frac{1}{2};\]

\[y_{2} = \frac{5 + 3}{2 \bullet 2} = 2;\]

\[x_{1} = \pm \frac{1}{\sqrt{2}} = \pm \frac{\sqrt{2}}{2};x_{2} = \pm \sqrt{2}.\]

\[Ответ:\ \ x_{1} = \pm \frac{\sqrt{2}}{2};\ \ x_{2} = \pm \sqrt{2}.\]