Решите систему неравенств x^2-5x+6<=0; 2x-5<=0.

Ответ:

\[\left\{ \begin{matrix} x^{2} - 5x + 6 \leq 0 \\ 2x - 5 \leq 0\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[x^{2} - 5x + 6 \leq 0\]

\[x_{1} + x_{2} = 5;\ \ \ x_{1} \cdot x_{2} = 6\]

\[x_{1} = 2;\ \ \ x_{2} = 3\]

\[(x - 2)(x - 3) \leq 0\]

\[2 \leq x \leq 3.\]

\[\left\{ \begin{matrix} 2 \leq x \leq 3 \\ 2x \leq 5\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} 2 \leq x \leq 3 \\ x \leq 2,5\ \ \ \ \\ \end{matrix} \right.\ \]

\[2 \leq x \leq 2,5.\]

\[Ответ:2 \leq x \leq 2,5.\]