Решите уравнение: 4y^4+7y^2-2=0.

Ответ:

\[4y^{4} + 7y^{2} - 2 = 0\]

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

\[4x^{2} + 7x - 2 = 0\]

\[D = 49 + 32 = 81\]

\[x_{1} = \frac{- 7 + 9}{8} = \frac{2}{8} = \frac{1}{4};\]

\[x_{2} = \frac{- 7 - 9}{8} = - 2 < 0.\]

\[y^{2} = \frac{1}{4}\]

\[y = \pm \frac{1}{2}.\]

\[Ответ:y = \pm \frac{1}{2}.\]