4, \(\sqrt{2x+5}=x+1\) (ĐK: \(x\ge-\dfrac{5}{2}\))
\(\Leftrightarrow2x+5=\left(x+1\right)^2\)
\(\Leftrightarrow2x+5=x^2+2x+1\)
\(\Leftrightarrow2x+5-x^2-2x-1\)
\(\Leftrightarrow-x^2+4=0\)
\(\Leftrightarrow-\left(x^2-4\right)=0\)
\(\Leftrightarrow-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-\left(x-2\right)=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)
5, \(\sqrt{5-x}=3x-1\) (ĐK: \(x\le5\))
\(\Leftrightarrow5-x=\left(3x-1\right)^2\)
\(\Leftrightarrow5-x=9x^2-6x+1\)
\(\Leftrightarrow5-x-9x^2+6x-1=0\)
\(\Leftrightarrow4+5x-9x^2=0\)
\(\Leftrightarrow-\left(x-1\right)\left(9x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\-\left(9x+4\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-\dfrac{4}{9}\left(tm\right)\end{matrix}\right.\)
