Question

Помогите пожалуйста решить систему уравнений. 30 б

Answer 1

18

$\begin{equation*}\begin{cases}\sqrt{x} + \sqrt{y} = 6 \\x - y = 12\end{cases}\end{equation*}\to\begin{equation*}\begin{cases}\sqrt{x} + \sqrt{y} = 6 \\(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y}) = 12\end{cases}\end{equation*} \to\begin{equation*}\begin{cases}\sqrt{x} + \sqrt{y} = 6 \\\sqrt{x} - \sqrt{y} = 2\end{cases}\end{equation*}$

И ответ:

$\begin{equation*}\begin{cases}\sqrt{x}= 4 \\\sqrt{y} = 2\end{cases}\end{equation*} \to \begin{equation*}\begin{cases}x= 16 \\y = 4\end{cases}\end{equation*}$

21

$\begin{equation*} \begin{cases} \sqrt[3]{x} - \sqrt[3]{y} = 3 \\ \sqrt[3]{x} + \sqrt[3]{y} = 5\end{cases}\end{equation*} \to \begin{equation*} \begin{cases} \sqrt[3]{x} = 4 \\ \sqrt[3]{y} = 1\end{cases}\end{equation*} \to \begin{equation*} \begin{cases} x= 64 \\ y = 1\end{cases}\end{equation*}$