Решебник по алгебре 7 класс Мерзляк ФГОС Задание 1202

 

\[\boxed{\text{1202\ (1202).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x + y = a,\ \ xy = b\]

\[1)\ x^{2} + y^{2} = a^{2} - 2b\]

\[a^{2} - 2b = (x + y)^{2} - 2xy =\]

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

\[= x^{2} + y^{2}\]

\[2)\ x^{3} + y^{3} = a^{3} - 3ab\]

\[a^{3} - 3ab =\]

\[= (x + y)^{3} - 3(x + y)xy =\]

\[= x^{3} + 3x^{2}y + 3xy^{2} + y^{3} - 3x^{2}y -\]

\[- 3xy^{2} = x^{3} + y^{3}\]

\[3)\ x^{4} + y^{4} = a^{4} - 4a^{2}b + 2b^{2}\]

\[так\ как\ x^{2} + y^{2} = a^{2} - 2b,\]

\[\text{\ \ }(x + y)^{2} = x^{2} + y^{2} + 2xy\]

\[\left( x^{2} + y^{2} \right)^{2} = \left( a^{2} - 2b \right)^{2}\]

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

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

\[x^{4} + y^{4} =\]

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

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

\[\boxed{\text{1202.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[x = - 2;\]

\[(0;0);\ \ (2;\ - 2)\ \]

\[y = \text{kx}\text{\ \ }\]

\[- 2 = 2k\text{\ \ }\]

\[k = - 1 \Longrightarrow \ \ y = - x;\]

\[(0;3);\ \ ( - 1;0)\]

\[y = kx + b\ \]

\[3 = 0 + b \Longrightarrow \ \ b = 3\]

\[0 = - k + 3\ \ \]

\[k = 3 \Longrightarrow \ \ y = 3x + 3.\]

\[(4;0),\ \ (0;\ - 2),\]

\[y = kx + b\]

\[\ - 2 = 0 + b \Longrightarrow \ \ b = - 2\]

\[0 = 4k - 2\]

\[4k = 2\ \]

\[k = 0,5 \Longrightarrow \ y = 0,5x - 2.\]