Question

Answer 1

\(1,\\ a,=\sqrt{9}\cdot\sqrt{64}=3\cdot8=24\\ b,=\sqrt{2}-1+4\sqrt{2}=5\sqrt{2}-1\\ c,=\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}=-\sqrt{6}\\ 2,\\ a,A=2\sqrt{x-2}-3\sqrt{x-2}+3\sqrt{x-2}=2\sqrt{x-2}\\ b,A=10\Leftrightarrow\sqrt{x-2}=5\Leftrightarrow x-2=25\Leftrightarrow x=27\\ 3,\\ a,P=\dfrac{x+9-6\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{\left(\sqrt{x}-3\right)^2}{\sqrt{x}\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-3}{\sqrt{x}}\\ b,\left|P\right|>P\Leftrightarrow P< 0\Leftrightarrow\dfrac{\sqrt{x}-3}{\sqrt{x}}< 0\\ \Leftrightarrow\sqrt{x}-3< 0\left(\sqrt{x}>0\right)\\ \Leftrightarrow0< x< 9\)