Question

giải hệ \(\left\{{}\begin{matrix}\sqrt{7x+y}+\sqrt{2x+y}=5\\x-y+\sqrt{2x+y}=1\end{matrix}\right.\)

Answer 1

Đặt \(\left\{{}\begin{matrix}\sqrt{7x+y}=a\\\sqrt{2x+y}=b\end{matrix}\right.\) thì ta có:

\(\left\{{}\begin{matrix}\sqrt{7x+y}+\sqrt{2x+y}=5\\5\left(x-y\right)+5\sqrt{2x+y}=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a+b=5\\3a^2-8b^2+5b=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=3\\b=2\end{matrix}\right.\)hoặc \(\left\{{}\begin{matrix}a=12\\b=-7\end{matrix}\right.\)(l)

\(\Rightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)