\[\boxed{\text{538\ (538).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[Пусть\ большее\ число\ \]
\[равняется\ x,\ а\ меньшее - y.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} x + y = 5 \cdot (x - y) \\ x^{2} - y^{2} = 180\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 4x = 6y\ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - y^{2} = 180 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = \frac{2}{3}\text{x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ x^{2} - \frac{4}{9}x^{2} = 180 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = \frac{2}{3}\text{x\ \ \ \ \ \ \ } \\ 5x^{2} = 1620 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} y = \frac{2}{3}\text{x\ \ \ \ } \\ x^{2} = 324 \\ \end{matrix} \right.\ \Longrightarrow\]
\[1)\ x_{1} = - 18 \Longrightarrow не\ \]
\[удовлетворяет\ услвоию,\ x > 0;\]
\[2)\ x_{2} = 18,\ \ y_{2} = 12.\]
\[Ответ:18\ и\ 12.\]
\[\boxed{\text{538.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ x² + x - 42 \leq 0\]
\[x^{2} + x - 42 = 0\]
\[x_{1} + x_{2} = - 1;\ \ \ \ \ x_{1} \cdot x_{2} = - 42\]
\[x_{1} = - 7;\ \ x_{2} = 6.\]
\[(x + 7)(x - 6) \leq 0\]
\[- 7 \leq x \leq 6.\]
\[\textbf{б)}\ (x + 11)(x + 4)(x - 1) > 0\]
\[x = - 11;\ \ x = - 4;\ \ x = 1\]
\[x \in ( - 11;\ - 4) \cup (1;\ + \infty).\]