Question

Giải hệ phương trình \(\left\{{}\begin{matrix}x+\sqrt{1-y^2}=1\\y+\sqrt{1-x^2}=1\end{matrix}\right.\)

Answer 1

ĐKXĐ:...

\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{1-y^2}=1-x\\\sqrt{1-x^2}=1-y\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}1-y^2=1-2x+x^2\\1-x^2=1-2y+y^2\end{matrix}\right.\)

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

Thay vào:

\(2x^2=2x\Rightarrow\left[{}\begin{matrix}x=y=0\\x=y=1\end{matrix}\right.\)