Đáp án:
$\begin{array}{l}
a)\sqrt {2016} - \sqrt {2015} \\
= \dfrac{{2016 - 2015}}{{\sqrt {2016} + \sqrt {2015} }}\\
= \dfrac{1}{{\sqrt {2016} + \sqrt {2015} }}\\
\sqrt {2015} - \sqrt {2014} \\
= \dfrac{{2015 - 2014}}{{\sqrt {2015} + \sqrt {2014} }}\\
= \dfrac{1}{{\sqrt {2015} + \sqrt {2014} }} > \dfrac{1}{{\sqrt {2016} + \sqrt {2015} }}\\
\Leftrightarrow \sqrt {2016} - \sqrt {2015} < \sqrt {2015} - \sqrt {2014} \\
b)\sqrt {2015} + \sqrt {2017} - 2\sqrt {2016} \\
= \sqrt {2017} - \sqrt {2016} - \left( {\sqrt {2016} - \sqrt {2015} } \right)\\
= \dfrac{{2017 - 2016}}{{\sqrt {2017} + \sqrt {2016} }} - \dfrac{{2016 - 2015}}{{\sqrt {2016} + \sqrt {2015} }}\\
= \dfrac{1}{{\sqrt {2017} + \sqrt {2016} }} - \dfrac{1}{{\sqrt {2016} + \sqrt {2015} }} < 0\\
\Leftrightarrow \sqrt {2015} + \sqrt {2017} < 2\sqrt {2016}
\end{array}$
