\[4x^{4} - 41x^{2} + 100 = 0\]
\[4x^{4} - 16x^{2} - 25x^{2} + 100 = 0\]
\[4x^{2}\left( x^{2} - 4 \right) - 25\left( x^{2} - 4 \right) = 0\]
\[\left( x^{2} - 4 \right)\left( 4x^{2} - 25 \right) = 0\]
\[1)\ x^{2} = 4\]
\[x = \pm 2.\]
\[2)\ 4x^{2} = 25\]
\[x^{2} = \frac{25}{4}\]
\[x = \pm \frac{5}{2} = \pm 2,5.\]
\[Ответ:x = \pm 2;x = \pm 2,5.\]