\(\sqrt{x+8+2\sqrt{x+7}}+\sqrt{x+8-2\sqrt{x+7}}=2\)
\(\Leftrightarrow\left|\sqrt{x+7}+1\right|+\left|\sqrt{x+7}-1\right|=2\)
\(\Leftrightarrow\sqrt{x+7}+1+\left|\sqrt{x+7}-1\right|=2\)
\(\Leftrightarrow\sqrt{x+7}+\left|\sqrt{x+7}-1\right|=1\)
\(\Leftrightarrow\left[{}\begin{matrix}2\sqrt{x+7}=2\left(x>=-6\right)\\1=1\left(-7< =x< -6\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-7< =x< =-6\\x+7=1\end{matrix}\right.\Leftrightarrow-7< =x< =-6\)
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