a: \(\Leftrightarrow\left[{}\begin{matrix}3x+2=4\\3x+2=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-2\end{matrix}\right.\)

\(a,=\left(2\sqrt{6}-4\sqrt{3}\right)\sqrt{6}+12\sqrt{2}=12-12\sqrt{2}+12\sqrt{2}=12\\ b,=\dfrac{6\left(3-\sqrt{3}\right)}{6}+\sqrt{3}=3-\sqrt{3}+\sqrt{3}=3\)

\(=\sqrt{8}\cdot\sqrt{8}-\sqrt[3]{\dfrac{16}{2}}=8-\sqrt[3]{8}=8-2=6\)

\(M=6\sqrt{2x}-\sqrt{2x}+2\sqrt{2x}-4\sqrt{2x}=3\sqrt{2x}\)

1)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)
2)
\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}\)
3)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)}=\sqrt{11}-\sqrt{5}\)
4)
\(=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
5)
\(=\sqrt{3^2-2.3.2\sqrt{2}+\left(2\sqrt{2}\right)^2}=\sqrt{\left(3-2\sqrt{2}\right)^2}=3-2\sqrt{2}\)

 

Để A>-2 thì \(-x+\sqrt{x}+2>0\)

\(\Leftrightarrow x-\sqrt{x}-2>0\)

\(\Leftrightarrow\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)>0\)

=>\(\sqrt{x}-2>0\)

=>x>4

f: \(\sqrt{\left(\sqrt2-\sqrt3\right)^2}-\frac{\sqrt6-3}{\sqrt2-\sqrt3}\)

\(=\left|\sqrt2-\sqrt3\right|-\frac{3-\sqrt6}{\sqrt3-\sqrt2}\)

\(=\sqrt3-\sqrt2-\frac{\sqrt3\left(\sqrt3-\sqrt2\right)}{\sqrt3-\sqrt2}=\sqrt3-\sqrt2-\sqrt3=-\sqrt2\)

g: \(\left(\sqrt8-3\sqrt2+\sqrt{10}\right)\left(\sqrt2-3\cdot\sqrt{0,4}\right)\)

\(=\left(2\sqrt2-3\sqrt2+\sqrt{10}\right)\left(\sqrt2-3\cdot\sqrt{0,4}\right)\)

\(=\left(-\sqrt2+\sqrt{10}\right)\left(\sqrt2-3\sqrt{0,4}\right)=2-3\sqrt{0,8}+\sqrt{20}-\sqrt4\)

\(=-3\sqrt{0,8}+2\sqrt5\)

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