Giải thích các bước giải:
$x+2y+1=\sqrt{2x-1}+5\sqrt{4y-23}$
$\rightarrow 2x+4y+2=2\sqrt{2x-1}+10\sqrt{4y-23}$
$\rightarrow 2x-1-2\sqrt{2x-1}+1+4y-23-10\sqrt{4y-23}+25=0$
$\rightarrow (\sqrt{2x-1}-1)^2+(\sqrt{4y-23}-5)^2=0$
Do $(\sqrt{2x-1}-1)^2+(\sqrt{4y-23}-5)^2\ge 0\quad\forall x\ge \dfrac{1}{2}, y\ge\dfrac{23}{4}$
$\rightarrow\begin{cases}\sqrt{2x-1}-1=0\rightarrow x=1\\ \sqrt{4y-23}-5=0\rightarrow y=12\end{cases}$