\(\sqrt{2x+1}=a;\text{ }\sqrt{4-x}=b\)
\(\Rightarrow x-1=\frac{a^2-b^2}{3}\)
\(pt\rightarrow a=b+\frac{a^2-b^2}{3}\Leftrightarrow3\left(a-b\right)=\left(a-b\right)\left(a+b\right)\)
\(\Leftrightarrow\left(a-b\right)\left(a+b-3\right)=0\Leftrightarrow\orbr{\begin{cases}a=b\\a+b=3\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{2x+1}=\sqrt{4-x}\\\sqrt{2x+1}+\sqrt{4-x}=3\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x+1=4-x\\2x+1+4-x+2\sqrt{2x+1}.\sqrt{4-x}=9\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=1\\2\sqrt{2x+1}.\sqrt{4-x}=-x+4\text{ }\left(1\right)\end{cases}}\)
\(\left(1\right)\Rightarrow4\left(2x+1\right)\left(4-x\right)=\left(-x+4\right)^2\)
\(\Leftrightarrow9x^2-36x=0\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)
\(KL:x\in\left\{0;1;4\right\}\)
\(VT=\sqrt{2x+1}+1\)
\(\Leftrightarrow\sqrt{2x+1}+1=x+\sqrt{4-x}\)
\(\Leftrightarrow\sqrt{2x+1}-x-\sqrt{4-x}+1=0\)
\(\Leftrightarrow x=\hept{\begin{cases}0\\1\\4\end{cases}}\)(trình bày thế cho nhanh)
