Lời giải:
1.
\(x=\sqrt{7-4\sqrt{3}}=\sqrt{(2-\sqrt{3})^2}=2-\sqrt{3}\)
\(S=x^2-3x-1=(7-4\sqrt{3})-3(2-\sqrt{3})-1\)
\(=-\sqrt{3}\)
2.
\(A=\frac{2013-2014}{\sqrt{2013}+\sqrt{2014}}=\frac{-1}{\sqrt{2013}+\sqrt{2014}}\)
\(B=\frac{2012-2013}{\sqrt{2012}+\sqrt{2013}}=\frac{-1}{\sqrt{2012}+\sqrt{2013}}\)
Dễ thấy $\sqrt{2013}+\sqrt{2014}> \sqrt{2012}+\sqrt{2013}$
$\Rightarrow \frac{1}{\sqrt{2013}+\sqrt{2014}}< \frac{1}{\sqrt{2012}+\sqrt{2013}}$
$\Rightarrow \frac{-1}{\sqrt{2013}+\sqrt{2014}}> \frac{-1}{\sqrt{2012}+\sqrt{2013}}$
Vậy $A>B$
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