Решебник по алгебре 7 класс Мерзляк Задание 457

\[\boxed{\text{457\ (457).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ 8x^{2} - 3 \cdot (x - 4) = 12\]

\[8x^{2} - 3x + 12 = 12\]

\[8x^{2} - 3x = 0\]

\[x \cdot (8x - 3) = 0\]

\[x = 0\ \ или\ \ 8x - 3 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{3}{8}.\]

\[Ответ:x = 0;\frac{3}{8}.\]

\[2)\ 5x^{3} - x \cdot (2x - 3) = 3x\]

\[5x^{3} - 2x^{2} + 3x = 3x\]

\[5x^{3} - 2x^{2} = 0\]

\[x^{2} \cdot (5x - 2) = 0\]

\[x = 0\ \ или\ \ 5x - 2 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = \frac{2}{5}.\]

\[Ответ:x = 0;\frac{2}{5}.\]

\[3)\ 4x - 0,2x \cdot (x + 20) = x^{3}\]

\[4x - 0,2x^{2} - 4x = x^{3}\]

\[- 0,2x^{2} - x^{3} = 0\]

\[- x^{2} \cdot (0,2 + x) = 0\]

\[x = 0\ \ или\ \ 0,2 + x = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 0,2.\]

\[Ответ:x = 0;\ - 0,2.\]

\[10x^{2} - 36x = 0\]

\[x \cdot (10x - 36) = 0\]

\[x = 0\ \ или\ \ 10x - 36 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 3,6.\]

\(Ответ:x = 0;3,6.\ \)