Question

giải hệ phương trình \(\left\{{}\begin{matrix}|x-1|+\frac{2}{\sqrt{y+1}}=4\\|2x-2|-\frac{1-2\sqrt{y+1}}{\sqrt{y+1}}=0\end{matrix}\right.\)

Answer 1

Lời giải:
HPT \(\Leftrightarrow \left\{\begin{matrix} |x-1|+\frac{2}{\sqrt{y+1}}=4\\ 2|x-1|-\frac{1}{\sqrt{y+1}}=-2\end{matrix}\right.\)

Đặt $|x-1|=a; \frac{1}{\sqrt{y+1}}=b$ thì hệ trở thành:

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

\(\Rightarrow 5a=4+-4=0\Rightarrow a=0\Leftrightarrow |x-1|=0\Rightarrow x=1\)

\(b=2a+2=2\Leftrightarrow \frac{1}{\sqrt{y+1}}=2\)

\(\Leftrightarrow y+1=\frac{1}{4}\Rightarrow y=-\frac{3}{4}\)

Vậy.......