Bài 1:
a)\(\sqrt{18}-2\sqrt{50}+3\sqrt{8}\) b)\(\left(\sqrt{7}-\sqrt{3}\right)^2+\sqrt{84}\) \(=3\sqrt{2}-2.5\sqrt{2}+3.4\sqrt{2}\) \(=7-2\sqrt{21}+3+2\sqrt{21}\) \(=5\sqrt{2}\) \(=10\) Bài 2. a)\(\sqrt{\left(2x+3\right)^2}=4\Rightarrow|2x+3|=4\) TH1:2x + 3=4 TH2:2x+3=-4 => 2x=1 =>2x=-7 =>\(x=\dfrac{1}{2}\). =>\(x=-\dfrac{7}{2}\)
b)\(\sqrt{9x}-5\sqrt{x}=6-4\sqrt{x}\) \(\Rightarrow3\sqrt{x}-5\sqrt{x}+4\sqrt{x}=6\) \(\Rightarrow2\sqrt{x}=6\Rightarrow\sqrt{x}=3\Rightarrow x=9\)
Câu 3:
ĐKXĐ: \(\left\{{}\begin{matrix}a>0\\a\ne1\end{matrix}\right.\)
Ta có: \(Q=\left(\dfrac{1}{\sqrt{a}+1}-\dfrac{1}{a+\sqrt{a}}\right):\dfrac{\sqrt{a}-1}{a+2\sqrt{a}+1}\)
\(=\dfrac{\sqrt{a}-1}{\sqrt{a}\left(\sqrt{a}+1\right)}\cdot\dfrac{\left(\sqrt{a}+1\right)^2}{\sqrt{a}-1}\)
\(=\dfrac{\sqrt{a}+1}{\sqrt{a}}\)
