Решебник по алгебре 8 класс Мерзляк ФГОС Задание 749

 

\[\boxed{\mathbf{749\ (749).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 7x + 10 =\]

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

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

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

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

\[2)\ y² + 3y - 4 =\]

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

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

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

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

\[3)\ a² + 8a + 12 =\]

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

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

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

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

\[4)\ x² - x - 6 =\]

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

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

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

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

\[\boxed{\mathbf{7}\mathbf{4}\mathbf{9}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² + bx + c = 0\]

\[x_{1} = - 2\]

\[x_{2} = 0,5\]

\[x_{1} + x_{2} = - b = - 2 + 0,5 = - 1,5,\ \ \]

\[b = 1,5\]

\[x_{1} \cdot x_{2} = c = - 2 \cdot 0,5 = - 1,\ \ \]

\[c = - 1\]

\[Ответ:b = 1,5;\ \ c = - 1.\]

\[2)x² + bx + c = 0\ \]

\[x_{1} = - 10\]

\[x_{2} = - 20\]

\[x_{1} + x_{2} = - b = - 10 - 20 =\]

\[= - 30,\ \ b = 30\]

\[x_{1} \cdot x_{2} = c = - 10 \cdot ( - 20) = 200,\ \ \]

\[c = 200\]

\[Ответ:\ b = 30;\ \ c = 200.\]