Question

So sánh:

A=\(\frac{2015}{\sqrt{2016}}+\frac{2016}{\sqrt{2015}}\) và B=\(\sqrt{2015}+\sqrt{2016}\)

Answer 1

Có: \(\sqrt{2015}< \sqrt{2016}\)

=>\(\frac{1}{\sqrt{2015}}>\frac{1}{\sqrt{2016}}\)

=>\(\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}>0\)

=>\(\sqrt{2015}+\sqrt{2016}+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}>\sqrt{2015}+\sqrt{2016}\)

=>\(\left(\sqrt{2015}+\frac{1}{\sqrt{2015}}\right)+\left(\sqrt{2016}-\frac{1}{\sqrt{2016}}\right)>\sqrt{2015}+\sqrt{2016}\)

=>\(\frac{2016}{\sqrt{2015}}+\frac{2015}{\sqrt{2016}}>\sqrt{2015}+\sqrt{2016}\)