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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 159
Задание 159
\[\boxed{\text{159\ (159).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Квадратное\ уравнение\ имеет\ \]
\[два\ различных\ корня\ \]
\[при\ D > 0.\]
\[1)\ ax^{2} + 2x - 1 = 0\]
\[D = 4 + 4a;\ \ \ a \neq 0\]
\[4 + 4a > 0\]
\[4a > - 4\]
\[a > - 1\]
\[Ответ:при\ a \in ( - 1; + \infty);\ \ \]
\[кроме\ 0.\]
\[2)\ (a + 1) \cdot x^{2} -\]
\[- (2a - 3) \cdot x + a = 0\]
\[D = (2a - 3)^{2} - 4a(a + 1) =\]
\[= 4a^{2} - 12a + 9 - 4a^{2} - 4a =\]
\[= - 16a + 9\]
\[a + 1 \neq 0,\ \ a \neq - 1\]
\[- 16a + 9 > 0\]
\[- 16a > - 9\]
\[a < \frac{9}{16}\]
\[Ответ:при\ a \in \left( \infty;\frac{9}{16} \right);\ \ \]
\[кроме - 1.\]
\[3)\ (a - 3)x^{2} - 2(a - 5)x +\]
\[+ a - 2 = 0\]
\[D = 4(a - 5)^{2} -\]
\[- 4(a - 3)(a - 2) = 4a^{2} -\]
\[- 40a + 100 - 4\left( a^{2} - 5a + 6 \right) =\]
\[= 4a^{2} - 40a + 100 - 4a^{2} +\]
\[+ 20a - 24 = - 20a + 76\]
\[- 20a + 76 > 0\]
\[- 20a > - 76\]
\[a < 3,8\ \ \]
\[a - 3 \neq 0,\ \ a \neq 3\]
\[Ответ:при\ a \in ( - \infty;3,8);\ \ \]
\[кроме\ 3.\]
\[\boxed{\text{159.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ 4x + y = 3\]
\[y = 3 - 4x\]
| \[x\] | \[0\] | \[1\] |
|---|---|---|
| \[y\] | \[3\] | \[- 1\] |
\[2)\ 2x - 3y = 6\]
\[2x - 6 = 3y\]
\[y = \frac{2x - 6}{3}\]
| \[x\] | \[0\] | \[3\] |
|---|---|---|
| \[y\] | \[- 2\] | \[0\] |
\[3)\ xy = - 8\]
\[y = - \frac{8}{x}\]
\[\ \]
| \[x\] | \[1\] | \[2\] | \[4\] | \[8\] | \[- 1\] | \[- 2\] | \[- 4\] | \[- 8\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[- 8\] | \[- 4\] | \[- 2\] | \[- 1\] | \[8\] | \[4\] | \[2\] | \[1\] |
\[4)\ (x - 2)^{2} + y^{2} = 0\]
\[5)\ (x - 3)(y - x) = 0\]
\[xy - x^{2} - 3y + 3x = 0\]
\[- x^{2} + 3x = 3y - xy\]
\[- x(x - 3) = y(3 - x)\]
\[y = \frac{x(x - 3)}{(x - 3)}\]
\[y = x;\ \ x \neq 3\]
\[6)\ \frac{y - x}{y^{2} - 1} = 0\]
\[\left\{ \begin{matrix} y = x\ \ \ \ \ \ \ \ \ \\ y^{2} - 1 \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} y = x\ \ \ \\ y \neq \pm 1 \\ \end{matrix} \right.\ \]
