ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1037

\[\boxed{\text{1037.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\textbf{а)}\ x² - 2xy + y^{2} + a^{2} =\]

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

\[(x - y)^{2} \geq 0\ \ \ и\ \ \ a^{2} \geq 0 \Longrightarrow\]

\[\Longrightarrow (x - y)^{2} + a² \geq 0.\]

\[\textbf{б)}\ 4x² + a² - 4x + 1 =\]

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

\[(2x - 1)^{2} \geq 0\ \ и\ \ \ a^{2} \geq 0 \Longrightarrow\]

\[\Longrightarrow (2x - 1)^{2} + a² \geq 0.\]

\[\textbf{в)}\ 9b² - 6b + 4c^{2} + 1 =\]

\[= (3b - 1)^{2} + 4c^{2}\ \]

\[(3b - 1)^{2} \geq 0\ \ и\ \ 4c^{2} \geq 0 \Longrightarrow\]

\[\Longrightarrow \ (3b - 1)^{2} + 4c² \geq 0.\]

\[\textbf{г)}\ a² + 2ab + 2b² + 2b + 1 =\]

\[= \left( a^{2} + 2ab + b \right) +\]

\[+ \left( b^{2} + 2b + 1 \right) =\]

\[= (a + b)^{2} + (b + 1)^{2},\ \ \]

\[(a + b)^{2} \geq 0\ \ \ и\ \ \ (b + 1)^{2} \geq 0\]

\[значит,\ \ (a + b)^{2} +\]

\[+ (b + 1)^{2} \geq 0.\]

\[\textbf{д)}\ x² - 4xy + y^{2} + x^{2}y^{2} + 1 =\]

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

\[+ \left( x^{2}y^{2} - 2xy + 1 \right) =\]

\[= (x - y)^{2} + (xy - 1)^{2}\]

\[(x - y)^{2} \geq 0\ \ \ и\ \ \]

\[(xy - 1)^{2} \geq 0 \Longrightarrow\]

\[\Longrightarrow (x - y)^{2} + (xy - 1)^{2}.\]

\[\textbf{е)}\ x² + y² + 2x + 6y + 10 =\]

\[= \left( x^{2} + 2x + 1 \right) +\]

\[+ \left( y^{2} + 6y + 9 \right) =\]

\[= (x + 1)^{2} + (y + 3)^{2}\text{\ \ }\]

\[(x + 1)^{2} \geq 0\ \ и\ \ \ (y + 3)^{2} \geq 0 \Longrightarrow\]

\[\Longrightarrow (x + 1)^{2} + (y + 3)^{2} \geq 0.\]