Question

giải pt : \(\sqrt{x+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}=4\)

Answer 1

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

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

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

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

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

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

\(\Rightarrow x=4\)

Answer 2