C1:\(\sqrt{x+\sqrt{x-4}}+\sqrt{x-\sqrt{x-4}}=0\)

\(\Rightarrow\sqrt{x-4+\sqrt{x-4}+4}+\sqrt{x-4-\sqrt{x-4}+4}=0\)

\(\Rightarrow\sqrt{\left(\sqrt{x-4}+2\right)^2}+\sqrt{\left(\sqrt{x-4}-2\right)^2}=0\)

\(\Rightarrow\sqrt{x-4}+2+\left|\sqrt{x-4}-2\right|=0\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x-4}+2+\sqrt{x-4}-2=0\\\sqrt{x-4}+2+2-\sqrt{x-4}=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2\sqrt{x-4}=0\Rightarrow\sqrt{x-4}=0\Rightarrow x-4=0\Rightarrow x=4\\4=0\Rightarrow vôlí\end{matrix}\right.\)

\(\Rightarrow x=4\)

b) Đặt \(\sqrt{x^2-6x+6}=a\left(a\ge0\right)\)

\(\Rightarrow a^2+3-4a=0\)

=> (a - 3).(a - 1) = 0

=> \(\left[{}\begin{matrix}a=3\\a=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\sqrt{x^2-6x+6}=3\\\sqrt{x^2-6x+6}=1\end{matrix}\right.\)

Bình phương lên giải tiếp nhé!

c) Tương tư câu b nhé