a: \(\Leftrightarrow\left|x-5\right|=6-x\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =6\\\left(6-x-x+5\right)\left(6-x+x-5\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< =6\\\left(-2x+11\right)\cdot1=0\end{matrix}\right.\Leftrightarrow x=\dfrac{11}{2}\left(loại\right)\)
b: \(\Leftrightarrow\sqrt{x-4+4\sqrt{x-4}+4}=2\)
\(\Leftrightarrow\left|\sqrt{x-4}+2\right|=2\)
\(\Leftrightarrow\sqrt{x-4}+2=2\)
=>x=4
c: \(\Leftrightarrow\left\{{}\begin{matrix}x^2-5x+6=x-2\\x-2>=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(x-2\right)^2=0\\x-2>=0\end{matrix}\right.\Leftrightarrow x=2\)
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