Question

Решите систему уравнении

Answer 1

$\begin{cases}x-y=8\\\sqrt x-\sqrt y=2\end{cases}\\\\O.D.3.\;\begin{cases}x\geq0\\y\geq0\end{cases}\\\\\sqrt x=a,\;\sqrt y=b\Rightarrow\begin{cases}a^2-b^2=8\\a-b=2\end{cases}\Rightarrow\begin{cases}a^2-(a-2)^2=8\\b=a-2\end{cases}\\\\\\a^2-(a-2)^2=8\\a^2-a^2+4a-4=8\\4a=12\\a=3\\\\\begin{cases}a=3\\b=1\end{cases}\\\\\begin{cases}\sqrt x=3\\\sqrt y=1\end{cases}\Rightarrow\begin{cases}x=9\\y=1\end{cases}$