Question

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

với giá trị nào của x thì A có nghĩa?

Answer 1

\(ĐK:\left\{{}\begin{matrix}x^2-1+2\sqrt{x^2-1}+1\ge0\\x^2-1-2\sqrt{x^2-1}+1\ge0\\x^2-1\ge0\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x^2-1}+1\right)^2\ge0\\\left(\sqrt{x^2-1}-1\right)^2\ge0\\x^2\ge1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x\ge1\\x\le-1\end{matrix}\right.\)

Answer 2

 

ĐK:⎧⎪⎨⎪⎩x2−1+2√x2−1+1≥0x2−1−2√x2−1+1≥0x2−1≥0⇔⎧⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪⎩(√x2−1+1)2≥0(√x2−1−1)2≥0x2≥1⇔[x≥1x≤−1