\(1,\\ 1,A=6\sqrt{2}-5\sqrt{2}-\sqrt{2}+1=1\\ 2,\\ a,P=\dfrac{\sqrt{a}+3+\sqrt{a}-3}{\left(\sqrt{a}-3\right)\left(\sqrt{a}+3\right)}\cdot\dfrac{\sqrt{a}-3}{\sqrt{a}}\\ P=\dfrac{2\sqrt{a}}{\sqrt{a}\left(\sqrt{a}+3\right)}=\dfrac{2}{\sqrt{a}+3}\\ b,P>\dfrac{1}{2}\Leftrightarrow\dfrac{2}{\sqrt{a}+3}-\dfrac{1}{2}>0\Leftrightarrow\dfrac{4-\sqrt{a}+3}{2\left(\sqrt{a}+3\right)}>0\\ \Leftrightarrow\dfrac{7-\sqrt{a}}{\sqrt{a}+3}>0\Leftrightarrow7-\sqrt{a}>0\left(\sqrt{a}+3>0\right)\\ \Leftrightarrow a< 49\)
\(C2,\\ 1,A=2\sqrt{3}+\sqrt{3}-\left(\sqrt{3}-1\right)=2\sqrt{3}+1\\ 2,\\ a,B=\dfrac{\sqrt{x}+1}{\sqrt{x}}\cdot\dfrac{\sqrt{x}-1+\sqrt{x}+1-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\\ B=\dfrac{2\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}=\dfrac{2}{\sqrt{x}}\\ b,B\in Z\Leftrightarrow\dfrac{2}{\sqrt{x}}\in Z\Leftrightarrow2⋮\sqrt{x}\\ \Leftrightarrow\sqrt{x}\inƯ\left(2\right)=\left\{1;2\right\}\left(\sqrt{x}>0\right)\\ \Leftrightarrow x\in\left\{1;4\right\}\)
\(3,\\ a,A=8\sqrt{3}-12\sqrt{3}+5\sqrt{3}+2\sqrt{3}=3\sqrt{3}\\ b,B=\dfrac{\sqrt{xy}\left(\sqrt{x}-\sqrt{y}\right)}{\sqrt{xy}}+\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)}{\sqrt{x}-\sqrt{y}}\\ B=\sqrt{x}-\sqrt{y}+\sqrt{x}+\sqrt{y}=2\sqrt{x}\)
