Решебник по алгебре 9 класс Мерзляк Задание 279

 

\[\boxed{\text{279\ (279).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[f(x) = (a - 1)x^{2} + 2ax + 6 - a\]

\[(a - 1)x^{2} + 2ax + 6 - a = 0\]

\[D = 4a^{2} - 4(a - 1)(6 - a) =\]

\[= 4a^{2} - 4\left( 7a - a^{2} - 6 \right) =\]

\[= {4a}^{2} - 28a + 4a^{2} + 24 =\]

\[= 8a^{2} - 28a + 24\]

\[Уравнение\ имеет\ один\ \]

\[корень\ при\ D = 0.\]

\[8a^{2} - 28a + 24 = 0\ \ \ \ \ \ \ |\ :4\]

\[2a^{2} - 7a + 6 = 0\]

\[D = 49 - 48 = 1\]

\[a = \frac{7 + 1}{4} = 2;\ \ a = \frac{7 - 1}{4} = 1,5.\]

\[При\ a = 1 - функция\ \]

\[является\ линейной:\]

\[a - 1 = 0\]

\[a = 1\]

\[Ответ:при\ a = 1,5;a = 2;a = 1.\ \]

\[\boxed{\text{279.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ y = |x + 4|\]

\[x \geq - 4:\]

\[y = x + 4\]

\[x \leq - 4:\]

\[y = - x - 4\]

\[2)\ y = |x - 5| + 2\]

\[x \geq 5:\]

\[y = x - 5 + 2 = x - 3\]

\[x < 5:\]

\[y = - x + 5 + 2 = - x + 7\]

\[3)\ y = |2x - 6| - x\]

\[x \geq 3:\]

\[y = 2x - 6 - x = x - 6\]

\[x < 3:\]

\[y = - 2x + 6 - x = - 3x + 6\]