\[\boxed{\text{266}\text{\ (266)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ (8x - 1)(2x - 3) -\]
\[- (4x - 1)^{2} = 38\]
\[16x^{2} - 24x - 2x + 3 - 16x^{2} +\]
\[+ 8x - 1 = 38\]
\[- 18x = 36\]
\[x = - 2.\]
\[Ответ:x = - 2.\]
\[\textbf{б)}\ \frac{(15x - 1)(15x + 1)}{3} = 2\frac{2}{3}\]
\[\frac{225x^{2} - 1}{3} = \frac{8}{3}\]
\[225x^{2} = 9\]
\[x^{2} = \frac{9}{225}\]
\[x = \pm \frac{3}{15} = \pm \frac{1}{5}\]
\[x = \pm 0,2\]
\[Ответ:x = \pm 0,2.\]
\[\textbf{в)}\ 0,5y^{3} - 0,5y(y + 1)(y - 3) =\]
\[= 7\]
\[y^{3} - y\left( y^{2} - 3y + y - 3 \right) = 14\]
\[y^{3} - y^{3} + 2y^{2} + 3y - 14 = 0\]
\[2y^{2} + 3y - 14 = 0\]
\[D = 9 + 4 \cdot 2 \cdot 14 = 121\]
\[y_{1,2} = \frac{- 3 \pm 11}{4} = 2;\ - 3,5.\]
\[Ответ:y = 2;\ \ y = - 3,5.\]
\[\textbf{г)}\ x^{4} - x^{2} = \frac{\left( 1 + 2x^{2} \right)\left( 2x^{2} - 1 \right)}{4}\]
\[4x^{4} - 4x^{2} = 4x^{4} - 1\]
\[4x^{2} = 1\]
\[x^{2} = \frac{1}{4}\]
\[x = \pm \frac{1}{2} = \pm 0,5\]
\[Ответ:x = \pm 0,5.\]