ĐKXĐ: ...
Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\ge0\\\sqrt{4-x}=b\ge0\end{matrix}\right.\)
\(\left(1-b^2\right)a+\left(1-a^2\right)b=-2a^2b^2+a^2+b^2\)
\(\Leftrightarrow\left(a+b\right)+2ab+2a^2b^2-ab\left(a+b\right)-\left(a+b\right)^2=0\)
\(\Leftrightarrow\left(a+b+2ab\right)-\left(a+b-ab\right)\left(a+b+2ab\right)=0\)
\(\Leftrightarrow\left(a+b+2ab\right)\left(a+b-ab-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a+b+2ab=0\left(vn\right)\\a+b-ab-1=0\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\left(a-1\right)\left(1-b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=1\\b=1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\sqrt{x+1}=1\\\sqrt{4-x}=1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
