Решите биквадратное уравнение: 16x^4– 25x² + 9 = 0.

Ответ:

\[16x^{4} - 25x^{2} + 9 = 0\]

\[Пусть\ x^{2} = y:\]

\[16y^{2} - 25y + 9 = 0\]

\[D = 625 - 576 = 49\]

\[y_{1} = \frac{25 + 7}{32} = 1;\]

\[y_{2} = \frac{25 - 7}{32} = \frac{18}{32} = \frac{9}{16}.\]

\[Подставим:\]

\[1)\ y = 1:\]

\[x^{2} = 1\]

\[x = \pm 1.\]

\[2)\ y = \frac{9}{16}:\]

\[x^{2} = \frac{9}{16}\]

\[x = \pm \frac{3}{4}.\]

\[Ответ:\ \ x = \pm 1;\ \ x = \pm \frac{3}{4}.\]