Question

Tìm Min A= \(\sqrt{x-1}+\sqrt{5-x}\)

Answer 1

Answer 2

\(A=\sqrt{x-1}+\sqrt{5-x}\)

Có: \(\left\{{}\begin{matrix}\sqrt{x-1}\ge0\forall x\\\sqrt{5-x}\ge0\forall x\end{matrix}\right.\)

\(\Rightarrow\sqrt{x-1}+\sqrt{5-x}\ge0\forall x\\ \Rightarrow A\ge0\forall x\\ \Rightarrow A_{min}=0\\ "="\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}=0\\\sqrt{5-x}=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x-1=0\\5-x=0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\x=5\end{matrix}\right.\)