a: ĐKXĐ: \(\left\{{}\begin{matrix}x^2-1>=0\\x^2+2\sqrt{x^2-1}>=0\\x^2-2\sqrt{x^2-1}>=0\end{matrix}\right.\)
=>\(x^2>=1\)
=>\(\left[{}\begin{matrix}x>=1\\x< =-1\end{matrix}\right.\)
b: \(A=\sqrt{x^2+2\sqrt{x^2-1}}-\sqrt{x^2-2\sqrt{x^2-1}}\)
\(=\sqrt{x^2-1+2\cdot\sqrt{x^2-1}\cdot1+1}-\sqrt{x^2-1-2\sqrt{x^2-1}\cdot1+1}\)
\(=\sqrt{\left(\sqrt{x^2-1}+1\right)^2}-\sqrt{\left(\sqrt{x^2-1}-1\right)^2}\)
\(=\sqrt{x^2-1}+1-\left|\sqrt{x^2-1}-1\right|\)
\(x>=\sqrt{2}\)
=>\(x^2>=2\)
=>\(\sqrt{x^2-1}>=\sqrt{2-1}=1\)
=>\(\sqrt{x^2-1}-1>=0\)
=>\(A=\sqrt{x^2-1}+1-\sqrt{x^2-1}+1=2\)
a.ĐK: \(x^2-1\ge0\Leftrightarrow\left[{}\begin{matrix}x\ge1\\x\le-1\end{matrix}\right.\)
\(b.A=\sqrt{x^2+2\sqrt{x^2-1}}-\sqrt{x^2-2\sqrt{x^2-1}}\\ =\sqrt{\left(x^2-1\right)+2\sqrt{x^2-1}\cdot1+1^2}-\sqrt{\left(x^2-1\right)-2\sqrt{x^2-1}\cdot1+1^2}\\ =\sqrt{\left(\sqrt{x^2-1}+1\right)^2}-\sqrt{\left(\sqrt{x^2-1}-1\right)^2}\\ =\sqrt{x^2-1}+1-\sqrt{x^2-1}+1=2\)
(vì x>= căn2)
