Решебник по алгебре 8 класс Мерзляк ФГОС Задание 765

 

\[\boxed{\mathbf{765\ (765).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ x² - 6xy + 5y^{2} =\]

\[= x^{2} + 9y^{2} - 6xy - 4y^{2} =\]

\[= (x - 3y)^{2} - 4y^{2} =\]

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

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

\[2)\ a² + 5ab - 36b^{2} =\]

\[= a^{2} - 4ab + 9ab - 36b^{2} =\]

\[= a(a + 9b) - 4b(a + 9b) =\]

\[= (a + 9b)(a - 4b)\]

\[3)\ 3m² - 8mn - 3n^{2} =\]

\[= 3m^{2} - 9mn + mn - 3n^{2} =\]

\[= 3m(m - 3n) + n(m - 3n) =\]

\[= (3m + n)(m - 3n)\]

\[4)\ 4x² - 5xy + y^{2} =\]

\[= 4x^{2} - 4xy - xy + y^{2} =\]

\[= 4x(x - y) - y(x - y) =\]

\[= (x - y)(4x - y)\]

\[\boxed{\mathbf{7}\mathbf{6}\mathbf{5}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[x^{2} + 4x + n = 0\]

\[3 \cdot \left( - 4 - x_{2} \right) - x_{2} = 8\]

\[- 12 - 3x_{2} - x_{2} = 8\]

\[- 4x_{2} = 20\]

\[x_{2} = - 5\]

\[x_{1} = - 4 - x_{2} = - 4 + 5 = 1\]

\[x_{1}x_{2} = n\]

\[- 5 \cdot 1 = - 5\]

\[Ответ:\ x_{1} = 1;\ \ x_{2} = - 5;\ \ \]

\[n = - 5.\]