Решите уравнение: y^4+9y^2=400.

\[y^{4} + 9y^{2} - 400 = 0\]

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

\[x^{2} + 9x^{2} - 400 = 0\]

\[D = 81 + 1600 = 1681 = 41^{2}\]

\[x_{1} = \frac{- 9 - 41}{2} = - 25 < 0;\]

\[x_{2} = \frac{- 9 + 41}{2} = \frac{32}{2} = 16.\]

\[y^{2} = 16\]

\[y = \pm 4.\]

\[Ответ:y = \pm 4.\]