Решите уравнение: 4x^4-3x^2-10=0.

Ответ:

\[4x^{4} - 3x^{2} - 10 = 0\]

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

\[4t^{2} - 3t - 10 = 0\]

\[D = 9 + 40 = 49\]

\[t_{1} = \frac{3 + 7}{8} = \frac{10}{8} = \frac{5}{4} = 1,25;\]

\[t_{2} = \frac{3 - 7}{8} = - \frac{4}{8} = - \frac{1}{2} < 0.\]

\[x^{2} = 1,25\]

\[x = \pm \sqrt{1,25} = \pm 0,5\sqrt{5}.\]

\[Ответ:x = \pm 0,5\sqrt{5}.\]