Решите биквадратное уравнение: 9x^4– 37x² + 4 = 0.

\[9x^{4} - 37x^{2} + 4 = 0\]

\[Пусть\ x^{2} = y \geq 0:\]

\[9y^{2} - 37y + 4 = 0\]

\[D = 1369 - 144 = 1225 = 35^{2}\]

\[y_{1} = \frac{37 + 35}{18} = \frac{72}{18} = 4;\]

\[y_{2} = \frac{37 - 35}{18} = \frac{2}{18} = \frac{1}{9}.\]

\[Подставим:\]

\[1)\ y = 4:\]

\[x^{2} = 4\]

\[x = \pm 2.\]

\[2)\ y = \frac{1}{9}:\]

\[x^{2} = \frac{1}{9}\]

\[x = \pm \frac{1}{3}\]

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