Решебник по алгебре 8 класс Мерзляк ФГОС Задание 763

 

\[\boxed{\mathbf{763\ (763)}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ y = \frac{x^{2} - 6x + 5}{x - 1}\]

\[x^{2} - 6x + 5 = 0\]

\[x_{1} + x_{2} = 6,\ \ x_{1} = 5\]

\[x_{1} \cdot x_{2} = 5,\ \ x_{2} = 1\]

\[x^{2} - 6x + 5 = (x - 5)(x - 1)\]

\[y = \frac{(x - 5)(x - 1)}{(x - 1)} = x - 5;\ \ \ \]

\[x \neq 1\]

\[y = x - 5,\ \ x \neq 1\ \]

\[2)\ y = \frac{3x^{2} - 10x + 3}{x - 3} - \frac{x^{2} - 4}{x + 2} =\]

\[= 3x - 1 - x + 2 = 2x + 1\]

\[3x^{2} - 10x + 3 = 0\]

\[x_{1} + x_{2} = \frac{10}{3},\ \ x_{1} = \frac{1}{3}\]

\[x_{1} \cdot x_{2} = 1,\ \ x_{2} = \frac{9}{3} = 3\]

\[y = 2x + 1;\ \ \ x \neq 3;\ \ x \neq - 2\]

\[\boxed{\mathbf{7}\mathbf{6}\mathbf{3}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[\frac{x_{1}}{x_{2}} = \frac{7}{3},\ \ 3x_{1} = 7x_{2},\ \ \]

\[x_{1} = \frac{7x_{2}}{3}\]

\[x^{2} + 20x + a = 0\]

\[x_{1} + x_{2} = - 20\]

\[\frac{7x_{2}}{3} + x_{2} = - 20\]

\[7x_{2} + 3x_{2} = - 60\]

\[10x_{2} = - 60\]

\[x_{2} = - 6\]

\[x_{1} = - 20 - x_{2} = - 20 + 6 =\]

\[= - 14\]

\[x_{1} \cdot x_{2} = a\]

\[- 6 \cdot ( - 14) = 84\]

\[Ответ:\ x_{1} = - 14;\ \ x_{2} = - 6;\ \ \]

\[a = 84.\]