Question

Rút gọn: A=\(\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x+1-4\sqrt{x-3}}\) với \(3\le x\le4\)

Answer 1

\(A=\sqrt{x-3-2\sqrt{x-3}+1}+\sqrt{x-3-4\sqrt{x-3}+4}\)

\(=\sqrt{\left(\sqrt{x-3}-1\right)^2}+\sqrt{\left(\sqrt{x-3}-2\right)^2}\)

\(=\left|\sqrt{x-3}-1\right|+\left|\sqrt{x-3}-2\right|\)

Do \(3\le x\le4\Rightarrow0\le\sqrt{x-3}\le1\)

\(\Rightarrow\left\{{}\begin{matrix}\sqrt{x-3}-1\le0\\\sqrt{x-3}-2< 0\end{matrix}\right.\)

\(\Rightarrow A=1-\sqrt{x-3}+2-\sqrt{x-3}=3-2\sqrt{x-3}\)