\[\boxed{\text{572}\text{\ (572)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 4x^{4} + 4x² - 15 = 0\]
\[Пусть\ t = x^{2},\ t \geq 0,\ тогда:\]
\[4t^{2} + 4t - 15 = 0\]
\[D = 4 + 4 \cdot 15 = 64\]
\[t_{1,2} = \frac{- 2 \pm 8}{4},\]
\[так\ как\ t \geq 0,\ то\ t = 1,5.\]
\[\Longrightarrow x^{2} = 1,5 \Longrightarrow x = \pm \sqrt{1,5}.\]
\[Ответ:x = \pm \sqrt{1,5}.\]
\[\textbf{б)}\ 2x^{4} - x^{2} - 36 = 0\]
\[Пусть\ t = x^{2},\ t \geq 0,\ тогда:\]
\[2t^{2} - t - 36 = 0\]
\[D = 1 + 4 \cdot 2 \cdot 36 = 289\]
\[t_{1,2} = \frac{1 \pm 17}{4},\]
\[так\ как\ t \geq 0,\ то\ \ t = 4,5;\]
\[x² = 4,5 \Longrightarrow x = \pm \sqrt{4,5}.\]
\[Ответ:x = \pm \sqrt{4,5}.\]