\(\sqrt{x^2+x+5}=x+1\left(Đk:x\ge-1\right)\)
\(x^2+x+5=x^2+2x+1\)
\(x=4\)
\(\sqrt{x^2+x+5}=x+1\left(x\ge-1\right)\\ \Leftrightarrow\sqrt{\left(x^2+x+5\right)^2}=\left(x+1\right)^2\\ \Leftrightarrow x^2+x+5=x^2+2x+1\\ \Leftrightarrow x^2+x-x^2-2x=1-5\\ \Leftrightarrow-x=-4\\ \Leftrightarrow x=4\left(tm\right)\)
\(\sqrt[]{x^2+x+5}=x+1\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1\ge0\\x^2+x+5=\left(x+1\right)^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x^2+x+5=x^2+2x+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge-1\\x=4\end{matrix}\right.\)
\(\Leftrightarrow x=4\)