Решебник по алгебре 8 класс Мерзляк ФГОС Задание 786

 

\[\boxed{\mathbf{786\ (786).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{2x - 13}{x - 6} = \frac{x + 6}{x}\]

\[\frac{2x - 13}{x - 6} - \frac{x + 6}{x} = 0\]

\[\frac{2x^{2} - 13x - x^{2} + 36}{x(x - 6)} = 0;\ \ \ \ \ \ \]

\[x \neq 0;\ \ \ \ x \neq 6\]

\[x^{2} - 13x + 36 = 0\]

\[x_{1} + x_{2} = 13,\ \ x_{1}x_{2} = 36,\ \]

\[\ x_{1} = 4,\ \ x_{2} = 9\]

\[Ответ:x = 4;x = 9.\]

\[3x^{2} - 4x - 20 =\]

\[= (2x - 5)(x + 2)\]

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

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

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

\[x_{2} = - 2\ (не\ подходит)\]

\[Ответ:x = 5.\]

\[\boxed{\mathbf{7}\mathbf{8}\mathbf{6}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 7x + 10 =\]

\[= \left( x^{2} - 4x + 4 \right) - 3x + 6 =\]

\[= (x - 2)^{2} - 3 \cdot (x - 2) =\]

\[= (x - 2)(x - 2 - 3) =\]

\[= (x - 2)(x - 5)\]

\[2)\ y² + 3y - 4 =\]

\[= \left( y^{2} + 8y + 16 \right) - 5y - 20 =\]

\[= (y + 4)^{2} - 5 \cdot (y + 4) =\]

\[= (y + 4)(y + 4 - 5) =\]

\[= (y + 4)(y - 1)\]

\[3)\ a² + 8a + 12 =\]

\[= \left( a^{2} + 4a + 4 \right) + 4a + 8 =\]

\[= (a + 2)^{2} + 4 \cdot (a + 2) =\]

\[= (a + 2)(a + 2 + 4) =\]

\[= (a + 2)(a + 6)\]

\[4)\ x² - x - 6 =\]

\[= \left( x^{2} - 6x + 9 \right) + 5x - 15 =\]

\[= (x - 3)^{2} + 5 \cdot (x - 3) =\]

\[= (x - 3)(x - 3 + 5) =\]

\[= (x - 3)(x + 2)\]