Question

Giải hệ phương trình sau:

8/ \(\left\{{}\begin{matrix}\sqrt{x+3}-2\sqrt{y+1}=2\\2\sqrt{x+3}+\sqrt{y+1}=4\end{matrix}\right.\)

Answer 1

Đặt \(\sqrt{x+3}=a\); \(\sqrt{y+1}=b\) (a,b \(\ge0\))

\(\Rightarrow\left\{{}\begin{matrix}a-2b=2\\2a+b=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2a-4b=4\\2a+b=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5b=0\\2a+b=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=0\\a=2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\sqrt{x+3}=2\\\sqrt{y+1}=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)(tmđk)

Vậy hệ pt có nghiệm suy nhất (x;y) = (1;-1)