Question

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

Answer 1

\(\sqrt{x-2\sqrt{x-1}}\) có nghĩa khi:

\(\left\{{}\begin{matrix}x-1\ge0\\x-2\sqrt{x-1}\ge0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x\ge2\sqrt{x-1}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\x^2\ge4\left(x-1\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge1\\\left(x-2\right)^2\ge0\left(LĐ\right)\end{matrix}\right.\)

\(\Rightarrow x\ge1.\)