Ta có :
\(\frac{2008}{\sqrt{2009}}+\frac{2009}{\sqrt{2008}}=\frac{2009}{\sqrt{2009}}-\frac{1}{\sqrt{2009}}+\frac{2008}{\sqrt{2008}}+\frac{1}{\sqrt{2008}}\)
\(=\sqrt{2008}+\sqrt{2009}+\frac{1}{\sqrt{2008}}-\frac{1}{\sqrt{2009}}\)
Mà \(\sqrt{2008}< \sqrt{2009}\Rightarrow\frac{1}{\sqrt{2008}}>\frac{1}{\sqrt{2009}}\Leftrightarrow\frac{1}{\sqrt{2008}}-\frac{1}{\sqrt{2009}}\)
\(\Leftrightarrow\sqrt{2008}+\sqrt{2009}+\frac{1}{\sqrt{2008}}-\frac{1}{\sqrt{2009}}>\sqrt{2008}+\sqrt{2009}\)
⇒ đpcm
so sánh \(\frac{2008}{\sqrt[]{2009}}+\frac{2009}{\sqrt[]{2008}}\) và \(\sqrt[]{2008}+\sqrt[]{2009}\)
So sánh 2008/căn 2009 + 2009/căn 2008 và căn 2008 + căn 2009
Cho A=\(\dfrac{2006}{2007}+\dfrac{2007}{2008}+\dfrac{2008}{2009}+\dfrac{2009}{2006}\) .Hãy so sánh số đó với 4
Cho hàm số f(x)=\(\frac{10^{2x}}{10^{2x}+10}\)
a)CMR:Nếu a,b là hai số thỏa mãn a+b=1thì f(a)+f(b)=1
b)Tính tổng:\(f\left(\frac{1}{2009}\right)+f\left(\frac{2}{2009}\right)+...+f\left(\frac{2008}{2009}\right)\)
\(\frac{x-1}{2001}\)+\(\frac{x-2}{2010}\)-\(\frac{x-3}{2009}\)=\(\frac{x-4}{2008}\)
\(\left|3x-5\right|=2009\left(2010^{2009}+2010^{2008}+...+2010+1\right)-2010^{2010}+5\)
chứng minh rằng
a, 2008 ^100 +2008^99 chia hết cho 2009
b, 12345^678 -12345^677 chia hết cho 12344
x-1/2011+x-2/2010-x-3/2009=x-4/2008
T=2^2010-(2^2009+2^2008+...+2^1+2^0)
