Câu 1.
\(5^2=25\)
\(\left(2\sqrt{6}\right)^2=24\)
Do \(25>24\) nên \(5>2\sqrt{6}\)
Câu 2
\(\sqrt{x^2}=5\)
\(\left|x\right|=5\)
\(x=5;x=-5\)
Câu 3
\(A=\sqrt{4x-4}+2\sqrt{x-1}-\sqrt{9x-9}\)
\(=2\sqrt{x-1}+2\sqrt{x-1}-3\sqrt{x-1}\)
\(=\sqrt{x-1}\)
Câu 4
ĐKXĐ: \(3-2x\ge0\Leftrightarrow x\le\dfrac{3}{2}\)
Câu 2
\(đkx\ge0\\ \sqrt{x^2}=5\\ x=5\left(thoaman\right)\\ Bài3\\ đkx\ge1\\ =2\sqrt{x-1}+2\sqrt{x-1}-3\sqrt{x-1}\\ =\sqrt{x-1}\\ Bài4\\ đk3-2x\ge0\\ x\le\dfrac{3}{2}\)
Câu 5
\(\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}+\dfrac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
\(=\dfrac{\left(\sqrt{7}+\sqrt{5}\right)^2+\left(\sqrt{7}-\sqrt{5}\right)^2}{\left(\sqrt{7}\right)^2-\left(\sqrt{5}\right)^2}\)
\(=\dfrac{7+2\sqrt{35}+5+7-2\sqrt{35}+5}{2}\)
\(=12\)