Question

tìm x để căn thức có nghĩa: √[x - 2√(x - 1)]

Answer 1

\(\sqrt{x-2\sqrt{x-1}}\)

\(\Rightarrow\left\{{}\begin{matrix}x-2\sqrt{x-1}\ge0\\x-1\ge0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x\ge2\sqrt{x-1}\\x\ge1\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x^2\ge4\left(x-1\right)^2\\x\ge1\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x^2-4x^2+8x-4\ge0\\x\ge1\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}\dfrac{2}{3}\le x\le2\\x\ge1\end{matrix}\right.\\ \Rightarrow\dfrac{2}{3}\le x\le2\)