1:
ĐKXĐ: \(-x^2+4x-2>=0\)
=>\(x^2-4x+2< =0\)
=>\(\left(x-2\right)^2-2< =0\)
=>\(-\sqrt{2}< =x-2< =\sqrt{2}\)
=>\(-\sqrt{2}+2< =x< =\sqrt{2}+2\)
\(\sqrt{-x^2+4x-2}=2-x\)
=>\(\left\{{}\begin{matrix}-x^2+4x-2=\left(2-x\right)^2\\2-x>=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x^2+4x-2=x^2-4x+4\\x< =2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x^2+8x-6=0\\2-\sqrt{2}< =x< =2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x^2-4x+3=0\\2-\sqrt{2}< =x< =2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(x-1\right)\left(x-3\right)=0\\2-\sqrt{2}< =x< =2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\in\left\{1;3\right\}\\2-\sqrt{2}< =x< =2\end{matrix}\right.\)
=>x=1
2: Bạn xem lại đề giúp mình nha, sao lại có 2 dấu bằng?
