\[\boxed{\text{424\ (424).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ y = x + 1;\ \ y = x - 1:\ \]
\[(x - y + 1)(y - x + 1) = 0.\]
\[\textbf{б)}\ y = x^{2};\ \ y = - 2:\]
\[\left( y - x^{2} \right)(y + 2) = 0.\]
\(\boxed{\text{424.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\)
\[Пусть\ a\ и\ b - катеты\ \]
\[треугольника.\ \]
\[Тогда\ его\ периметр:\ \ \]
\[a + b + 37 = 84.\]
\[По\ теореме\ Пифагора:\]
\[a^{2} + b^{2} = 37^{2}.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} a^{2} + b^{2} = 37^{2}\text{\ \ } \\ a + b + 37 = 84 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (47 - b)^{2} + b^{2} = 37^{2} \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2209 - 94b + b^{2} + b^{2} = 1369 \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} a = 47 - b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2b^{2} - 94b + 840 = 0 \\ \end{matrix} \right.\ \]
\[b^{2} - 47b + 420 = 0\]
\[D = 47^{2} - 4 \cdot 420 = 526\]
\[b_{1,2} = \frac{47 \pm 23}{2} = 35;12.\]
\[\left\{ \begin{matrix} b_{1} = 35 \\ a_{1} = 12 \\ \end{matrix} \right.\ \ \ \ или\ \ \ \left\{ \begin{matrix} b_{2} = 12 \\ a_{2} = 35 \\ \end{matrix} \right.\ ;\ \ \]
\[S = \frac{1}{2} \cdot a \cdot b =\]
\[= \frac{12 \cdot 35}{2} = 210\ \left( см^{2} \right).\]
\[Ответ:210\ см^{2}.\]