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МатематикаРешебник по алгебре 9 класс Мерзляк Задание 445
Задание 445
\[\boxed{\text{445\ (445).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ 4x + y = 3\]
\[y = 3 - 4x\]
| \[x\] | \[0\] | \[1\] |
|---|---|---|
| \[y\] | \[3\] | \[- 1\] |
\[2)\ 2x - 3y = 6\]
\[2x - 6 = 3y\]
\[y = \frac{2x - 6}{3}\]
| \[x\] | \[0\] | \[3\] |
|---|---|---|
| \[y\] | \[- 2\] | \[0\] |
\[3)\ xy = - 8\]
\[y = - \frac{8}{x}\]
\[\ \]
| \[x\] | \[1\] | \[2\] | \[4\] | \[8\] | \[- 1\] | \[- 2\] | \[- 4\] | \[- 8\] |
|---|---|---|---|---|---|---|---|---|
| \[y\] | \[- 8\] | \[- 4\] | \[- 2\] | \[- 1\] | \[8\] | \[4\] | \[2\] | \[1\] |
\[4)\ (x - 2)^{2} + y^{2} = 0\]
\[5)\ (x - 2)^{2} + (y + 1)^{2} = 9\]
\[\text{O\ }(0;0);\ r = 3\]
\[6)\ x^{2} + y^{2} = 4\]
\[\text{O\ }(0;0);\ \ r = 2.\]
\(\ \)
\[7)\ x^{2} + 2x + y^{2} - 6y + 10 = 0\]
\[\left( x^{2} + 2x + 1 \right) +\]
\[+ \left( y^{2} - 6y + 9 \right) = 0\]
\[(x + 1)^{2} + (y - 3)^{2} = 0\]
\[\text{O\ }( - 1;3).\]
\[8)\ (x - 3)(y - x) = 0\]
\[xy - x^{2} - 3y + 3x = 0\]
\[- x^{2} + 3x = 3y - xy\]
\[- x(x - 3) = y(3 - x)\]
\[y = \frac{x(x - 3)}{(x - 3)}\]
\[y = x;\ \ x \neq 3\]
\[9)\ \frac{y - x}{y^{2} - 1} = 0\]
\[\left\{ \begin{matrix} y = x\ \ \ \ \ \ \ \ \ \\ y^{2} - 1 \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} y = x\ \ \ \\ y \neq \pm 1 \\ \end{matrix} \right.\ \]
\[\boxed{\text{445.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = 3x^{2} - 18x + 2\]
\[1)\ \lbrack - 1;4\rbrack\]
\[y( - 1) = 3 + 18 + 2 = 23\ \ \]
\[y(0) = 2\]
\[y(1) = 3 - 18 + 2 = - 13\]
\[y(2) = 12 - 36 + 2 = - 22\]
\[y(3) = 27 - 54 + 2 = - 25\]
\[y(4) = 48 - 72 + 2 = - 22.\]
\[Ответ:\ y_{\min} = - 25.\]
\[2)\ \lbrack - 4;1\rbrack\]
\[y( - 4) = 48 + 72 + 2 = 122\]
\[y( - 3) = 27 + 54 + 2 = 83\]
\[y( - 2) = 12 + 36 + 2 = 50\ \ \]
\[y( - 1) = 3 + 18 + 2 = 23\]
\[y(0) = 2\ \ \]
\[y(1) = 3 - 18 + 2 = - 13.\]
\[Ответ:\ y_{\min} = - 13.\]
\[3)\ \lbrack 4;5\rbrack\]
\[y(4) = 48 - 72 + 2 = - 22\]
\[y(5) = 75 - 90 + 2 = - 13.\]
\[Ответ:\ y_{\min} = - 22.\]
