\[\boxed{\text{897.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ 9a + \frac{1}{a} \geq 6,\ \ a > 0\]
\[9a + \frac{1}{a} - 6 \geq 0\]
\[\frac{9a \cdot a + 1 - 6 \cdot a}{a} \geq 0\]
\[\frac{9a^{2} + 1 - 6a}{a} \geq 0\]
\[\frac{(3a - 1)²}{a} \geq 0 \Longrightarrow ч.т.д.\]
\[\textbf{б)}\ 25b + \frac{1}{b} \leq - 10,\ \ b < 0\]
\[25b + \frac{1}{b} + 10 \leq 0\]
\[\frac{25b \cdot b + 1 + 10 \cdot b}{b} \leq 0\]
\[\frac{25b^{2} + 1 + 10b}{b} \leq 0\ \]
\[\frac{(5b + 1)^{2}}{b} \leq 0\ \ \ \ |\ :b\ (b < 0)\]
\[(5b + 1)^{2} \geq 0,\ \ b < 0.\]