Решите уравнение: a^4+2a^2-8=0.

\[a^{4} + 2a^{2} - 8 = 0\]

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

\[x^{2} + 2x - 8 = 0\]

\[D_{1} = 1 + 8 = 9\]

\[x_{1} = - 1 + 3 = 2;\ \]

\[x_{2} = - 1 - 3 = - 4 < 0.\]

\[a^{2} = 2\]

\[a = \pm \sqrt{2}.\]

\[Ответ:a = \pm \sqrt{2}.\]