Đặt \(\left\{{}\begin{matrix}a=\sqrt{1-x}\ge0\\b=\sqrt{1+x}\ge0\end{matrix}\right.\)
Ta được hệ pt
\(\left\{{}\begin{matrix}a^2+b^2=2\\a+b+2ab=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(a+b\right)^2-2ab=2\\a+b+2ab=4\end{matrix}\right.\)
Cộng theo vế 2 pt trên, ta có:
\(\left(a+b\right)^2+\left(a+b\right)=6\)
\(\Leftrightarrow\left(a+b\right)^2+\left(a+b\right)-6=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a+b=2\\a+b=-3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a+b=2\\ab=1\end{matrix}\right.\\\left\{{}\begin{matrix}a+b=-3\\ab=\dfrac{7}{2}\end{matrix}\right.\end{matrix}\right.\)
Đến đây dễ rồi nhé ^^
