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МатематикаГДЗ по алгебре 8 класс Мерзляк Задание 219
Задание 219
\[\boxed{\text{219\ (219).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{x - 1}{x - a} = 0\]
\[если\ a \neq 1:\]
\[x - 1 = 0\]
\[\ x = 1.\]
\[если\ a = 1:\]
\[\frac{x - 1}{x - 1} = 0\ \ \]
\[1 \neq 0 - корней\ нет.\]
\[2)\ \frac{x - a}{x + 5} = 0\]
\[если\ a \neq - 5:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x \neq - 5\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]
\[x = a.\]
\[если\ a = - 5:\]
\[\frac{x + 5}{x + 5} = 0\ \ \]
\[1 \neq 0 - корней\ нет.\]
\[3)\ \frac{a(x - a)}{x - 3} = 0\]
\[если\ a = 0:\ \]
\[\frac{0}{x - 3} = 0\ \ \]
\[\left\{ \begin{matrix} x - любое\ число \\ x \neq 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ .\]
\[если\ a \neq 0;\ \ a \neq 3\]
\[\left\{ \begin{matrix} x - a = 0 \\ x - 3 \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = a \\ x \neq 3 \\ \end{matrix} \right.\ \ \]
\[x = a.\]
\[если\ a = 3:\]
\[\frac{3(x - 3)}{x - 3} = 0\]
\[1 \neq 0 - корней\ нет.\]
\[4)\ \frac{(x - a)(x - 6)}{x - 7} = 0\]
\[если\ a \neq 7:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x - 6 = 0 \\ x \neq 7\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ }\]
\[\left\{ \begin{matrix} x = a \\ x \neq 7 \\ \end{matrix} \right.\ \ \]
\[x = a\ или\ x = 6.\]
\[если\ a = 7:\]
\[\frac{(x - 7)(x - 6)}{x - 7} = 0\ \ \]
\[\left\{ \begin{matrix} x = 6 \\ x \neq 7 \\ \end{matrix} \right.\ \text{\ \ }\]
\[x = 6.\]
\[5)\ \frac{(x - 4)(x + 2)}{x - a} = 0\]
\[если\ a \neq 4\ и\ a \neq - 2:\]
\[\left\{ \begin{matrix} x - 4 = 0 \\ x + 2 = 0 \\ \end{matrix} \right.\ \]
\[x = 4\ или\ x = - 2.\]
\[если\ a = 4:\ \ \]
\[\frac{(x - 4)(x + 2)}{(x - 4)} = 0\ \ \]
\[x + 2 = 0\ \ \]
\[x = - 2.\]
\[если\ a = - 2:\]
\[\frac{(x - 4)(x + 2)}{x + 2} = 0\ \ \]
\[x - 4 = 0\]
\[x = 4.\]
\[6)\ \frac{x - a}{(x - 4)(x + 2)} = 0\]
\[если\ a \neq 4\ и\ a \neq - 2:\]
\[\left\{ \begin{matrix} x - a = 0 \\ x \neq 4\ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix} \right.\ \]
\[x = a.\]
\[если\ a = 4:\ \]
\[\frac{x - 4}{(x - 4)(x + 2)} = 0\]
\[\left\{ \begin{matrix} x - 4 = 0 \\ x \neq 4\ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix}\ \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = 4\ \ \ \\ x \neq 4\ \ \ \\ x \neq - 2\ \\ \end{matrix} \right.\ \]
\[корней\ нет.\]
\[если\ a = - 2:\]
\[\frac{x + 2}{(x - 4)(x + 2)} = 0\ \]
\[\left\{ \begin{matrix} x + 2 = 0 \\ x \neq 4\ \ \ \ \ \ \ \ \\ x \neq - 2\ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }\left\{ \begin{matrix} x = - 2 \\ x \neq 4\ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]
\[корней\ нет.\]
