\[\boxed{\text{1024.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ a² + ab + b² \geq 0\]
\[a² + 2ab + b² - ab \geq 0\]
\[(a + b)^{2} - ab \geq 0\]
\[(a + b)^{2} \geq ab \Longrightarrow ч.т.д.\]
\[\textbf{б)}\ a² - ab + b^{2} \geq 0\]
\[a² - 2ab + b^{2} + ab \geq 0\]
\[(a - b)^{2} \geq - ab \Longrightarrow ч.т.д.\]