Question

Tìm tất cả nghiệm của cặp phương trình \(\left\{{}\begin{matrix}5\left|x+1\right|-3\left|y-2\right|=7\\2\sqrt{4x^2+8x+4}+5\sqrt{y^2-4y+4}=13\end{matrix}\right.\).

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}5\left|x+1\right|-3\left|y-2\right|=7\\4\sqrt{\left(x+1\right)^2}+5\sqrt{\left(y-2\right)^2}=13\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5\left|x+1\right|-3\left|y-2\right|=7\\4\left|x+1\right|+5\left|y-2\right|=13\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\left|x+1\right|=2\\\left|y-2\right|=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=\left\{1;-3\right\}\\y=\left\{3;1\right\}\end{matrix}\right.\)

\(\Rightarrow\left(x;y\right)=\left(1;3\right);\left(1;1\right);\left(-3;3\right);\left(-3;1\right)\)