1.\(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}=\frac{\sqrt{7}\left(\sqrt{2}-1\right)}{-\left(\sqrt{2}-1\right)}=-\sqrt{7}\)
2.
ĐK: \(x\ge0\)
a, \(A=2\sqrt{12x}-4\sqrt{3x}+27-3\sqrt{27x}\)
\(=2\sqrt{2^2\cdot3x}-4\sqrt{3x}+27-3\sqrt{3^2\cdot3x}\)
\(=4\sqrt{3x}-4\sqrt{3x}+27-9\sqrt{3x}=27-9\sqrt{3x}\)
b,
\(A=27-9\sqrt{3x}\le27-9\sqrt{3\cdot0}=27\)
\(A_{max}=27\Leftrightarrow x=0\)