Câu 1)
a) \(\sqrt{18}+2\sqrt{45}-3\sqrt{80}-2\sqrt{50}=\sqrt{9.2}+2\sqrt{9.5}-3\sqrt{16.5}-2\sqrt{25.2}=3\sqrt{2}+6\sqrt{5}-12\sqrt{5}-10\sqrt{2}=-7\sqrt{2}-6\sqrt{5}\)
b) ĐK: \(x\ge2\)
\(\sqrt{x-2}=3\Leftrightarrow\left(\sqrt{x-2}\right)^2=3^2\Leftrightarrow x-2=9\Leftrightarrow x=11\left(tm\right)\)
Vậy S={11}
Câu 2)
a) Để p xác định thì \(\left\{{}\begin{matrix}\sqrt{x}-2\ne0\\x\ge0\\x\ne4\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)
b) \(p=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\right):\dfrac{2x}{x-4}=\left[\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right].\dfrac{x-4}{2x}=\dfrac{\sqrt{x}+2+\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{2x}=\dfrac{2\sqrt{x}}{2x}=\dfrac{1}{\sqrt{x}}\)
c) Ta có \(p< 1\Leftrightarrow\dfrac{1}{\sqrt{x}}< 1\Leftrightarrow\sqrt{x}>1\Leftrightarrow x>1\)
Kết hợp với ĐKXĐ, vậy \(x>1\) và \(x\ne4\) thì p<1
