Решебник по алгебре 7 класс Мерзляк ФГОС Задание 870

 

\[\boxed{\text{870\ (870).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\ y = 2,5x + 10\]

\[2,5x + 10 = 0\]

\[2,5x = - 10\]

\[x = - 4,\ \ ( - 4;0)\]

\[Ответ:( - 4;0);\ \ (0;10).\]

\[2)\ y = 6x - 4\]

\[y = 6 \cdot 0 - 4 = - 4,\ \ (0;\ - 4)\]

\[6x - 4 = 0\]

\[6x = 4\]

\[x = \frac{2}{3},\ \ \left( \frac{2}{3};0 \right)\]

\[Ответ:(0;\ - 4),\ \left( \frac{2}{3};0 \right)\text{.\ }\]

\[\boxed{\text{870.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[(a + b + c)^{3} - a^{3} - b^{3} - c^{3} =\]

\[= \left( (a + b + c)^{3} - a^{3} \right) - \left( b^{3} + c^{3} \right) =\]

\[- (b + c)\left( b^{2} - cb + c^{2} \right) =\]

\[= 3 \cdot (b + c)(a + b)(a + c)\]

\[3 \cdot (b + c)(a + b)(a + c) =\]

\[= 3 \cdot (b + c)(a + b)(a + c) \Longrightarrow\]

\[\Longrightarrow тождество\ верно.\]

\[(a - b)^{3} + (b - c)^{3} - (a - c)^{3} =\]

\[= 3(a - c)(b - a)(b - c) =\]

\[= - 3(a - c)(a - b)(b - c)\]

\[- 3(a - c)(a - b)(b - c) =\]

\[= - 3(a - c)(a - b)(b - c) \Longrightarrow\]

\[\Longrightarrow тождество\ верно.\]