\[\boxed{\text{525\ (525).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ x^{4} = 81\]
\[3^{4} = 81\]
\[( - 3)^{4} = 81\]
\[x = \pm 3\]
\[Ответ:x = \pm 3.\]
\[\textbf{б)}\ x^{6} = 64\]
\[2^{6} = 64\]
\[( - 2)^{6} = 64\]
\[x = \pm 2\]
\[Ответ:x = \pm 2.\]
\[\textbf{в)}\ x^{2} - x = 2\]
\[x(x - 1) = 2\]
\[x = 2;\ \ \ x = - 1\]
\[Ответ:x = 2;\ \ x = - 1.\]
\[\textbf{г)}\ x^{4} + x^{3} = 6x^{2}\ \ \ |\ :x^{2}\]
\[x^{2} + x = 6\]
\[x(x + 1) = 6\]
\[x = - 3;\ \ x = 2\]
\[Ответ:x = - 3;x = 2.\]
\[\textbf{д)}\ x^{3} - 3x^{2} - 4x + 12 = 0\]
\[x^{2}(x - 3) - 4 \cdot (x - 3) = 0\]
\[(x - 3)\left( x^{2} - 4 \right) = 0\]
\[(x - 3)(x - 2)(x + 2) = 0\]
\[x = 3;\ \ x = 2;\ \ x = - 2\]
\[Ответ:x = \pm 2;\ \ x = 3.\]
\[\textbf{е)}\ x^{3} + 3x^{2} - x - 3 = 0\]
\[x\left( x^{2} - 1 \right) + 3 \cdot \left( x^{2} - 1 \right) = 0\]
\[\left( x^{2} - 1 \right)(x + 3) = 0\]
\[(x - 1)(x + 1)(x + 3) = 0\]
\[x = 1;\ \ x = - 1;\ \ x = - 3\]
\[Ответ:x = \pm 1;\ \ x = - 3.\ \]