Ta có

\(\hept{\begin{cases}\sqrt{2008}+\sqrt{2005}< \sqrt{2015}+\sqrt{2009}\left(1\right)\\\sqrt{2010}+\sqrt{2007}< \sqrt{2015}+\sqrt{2009}\left(2\right)\end{cases}}\)

\(\Rightarrow\frac{1}{\sqrt{2008}+\sqrt{2005}}+\frac{1}{\sqrt{2010}+\sqrt{2007}}>\frac{2}{\sqrt{2015}+\sqrt{2009}}\)

\(\Leftrightarrow\frac{\sqrt{2008}-\sqrt{2005}}{3}+\frac{\sqrt{2010}-\sqrt{2007}}{3}>\frac{\sqrt{2015}-\sqrt{2009}}{3}\)

\(\Leftrightarrow\sqrt{2008}+\sqrt{2009}+\sqrt{2010}>\sqrt{2005}+\sqrt{2007}+\sqrt{2015}\)

A=√2008+√2009+√2010A=2008+2009+2010 và B=√2005+√2007+√2015

k và kb với mình nha !!!

tính cụ thể từng cái ra

a. Ta có \(\sqrt{2016}+\sqrt{2015}>\sqrt{2015}+\sqrt{2014}\to\frac{1}{\sqrt{2016}+\sqrt{2015}}

khos

\(C=\sqrt[3]{2011}-\sqrt[3]{2010}=\frac{2011-2010}{\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)}=\frac{1}{\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)}\)

\(B=\sqrt[3]{2010}-\sqrt[3]{2009}=\frac{2010-2009}{\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)}=\frac{1}{\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)}\)Vì \(\left(\sqrt[3]{2011^2}+\sqrt[3]{2011}\sqrt[3]{2010}+\sqrt[3]{2010^2}\right)>\left(\sqrt[3]{2010^2}+\sqrt[3]{2010}\sqrt[3]{2009}+\sqrt[3]{2009^2}\right)\)

\(B< C\)

lập phương B , C lên 

Không tính giá trị đâu mấy cậu. Tuôi vừa nghĩ ra, lấy \(C-B=\sqrt[3]{2011}-\sqrt[3]{2009}>0.\)Dẫn tới  C>B.

\(\sqrt{2009}-\sqrt{2008}

\(\frac{1}{\sqrt{2009}-\sqrt{2008}}=\frac{\sqrt{2009}+\sqrt{2008}}{\left(\sqrt{2009}+\sqrt{2008}\right)\left(\sqrt{2009}-\sqrt{2008}\right)}=\frac{\sqrt{2009}+\sqrt{2008}}{2009-2008}=\sqrt{2009}+\sqrt{2008}\)

CMTT : \(\frac{1}{\sqrt{2008}-\sqrt{2007}}=\sqrt{2008}+\sqrt{2007}\)

Vì \(\sqrt{2009}+\sqrt{2008}>\sqrt{2008}+\sqrt{2007}\)

=> \(\frac{1}{\sqrt{2009}-\sqrt{2008}}\sqrt{2008}-\sqrt{2007}\)