ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 1017

\[\boxed{\text{1017.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[\textbf{а)}\ a² + b² + 2 \geq 2 \cdot (a + b)\]

\[a² + b² + 2 - 2a - 2b \geq 0\]

\[\left( a^{2} - 2a + 1 \right) +\]

\[+ \left( b^{2} - 2b + 1 \right) \geq 0\]

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

\[(a - 1)^{2} \geq 0,\ \ (b - 1)^{2} \geq 0\]

\[то\ есть\ a^{2} + b^{2} + 2 \geq\]

\[\geq 2 \cdot (a + b) \Longrightarrow ч.т.д.\]

\[\textbf{б)}\ a² + b² + c² +\]

\[+ 5 > 2 \cdot (a + b + c)\]

\[a^{2} + b^{2} + c^{2} + 5 - 2a -\]

\[- 2b - 2c > 0\]

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

\[+ \left( c^{2} - 2c + 1 \right) + 2 > 0\]

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

\[+ (c - 1)^{2} + 2 > 0\]

\[(a - 1)^{2} \geq 0,\ \ (b - 1)^{2} \geq 0,\]

\[\text{\ \ }(c - 1)^{2} \geq 0,\ \ 2 > 0\]

\[то\ есть\ a^{2} + b^{2} + c^{2} + 5 >\]

\[> 2 \cdot (a + b + c) \Longrightarrow ч.т.д.\]