Решите уравнение: x^4-x^2+3/16=0.

\[x^{4} - x^{2} + \frac{3}{16} = 0\ \ \ \ \ \ \ | \cdot 16\ \]

\[16x^{4} - 16x^{2} + 3 = 0\]

\[t = x^{2};\ \ \ \ \ t \geq 0\]

\[16t^{2} - 16t + 3 = 0\]

\[D = ( - 16)^{2} - 4 \cdot 16 \cdot 3 =\]

\[= 256 - 192 = 64;\ \ \ \ \ \sqrt{D} = 8.\]

\[t_{1} = \frac{16 + 8}{2 \cdot 16} = \frac{24}{32} = \frac{3}{4};\ \ \ \ \]

\[\text{\ \ \ }t_{2} = \frac{16 - 8}{2 \cdot 16} = \frac{8}{32} = \frac{1}{4}\]

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