ГДЗ по алгебре 8 класс Макарычев Задание 578

\[\textbf{а)}\ \frac{x(x - 3)}{6} - \frac{x}{2} = 0\ \ \ \ \ \ | \cdot 6\]

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

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

\[x^{2} - 6x = 0\]

\[x(x - 6) = 0\]

\[x = 0,\ \ x = 6\]

\[Ответ:x = 0;\ \ x = 6.\]

\[\textbf{б)}\ \frac{\text{\ x}(x + 1)}{3} + \frac{8 + x}{4} = 2\ \ \ \ \ \ | \cdot 12\]

\[4x(x + 1) + 3(8 + x) = 24\]

\[4x^{2} + 4x + 24 + 3x = 24\]

\[4x^{2} + 7x = 0\]

\[x(4x + 7) = 0\]

\[x = 0\ \ \ \ \ \ 4x + 7 = 0\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4x = - 7\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - \frac{7}{4}\]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 1,75\ \]

\[Ответ:x = 0;\ \ x = - 1,75.\]