\(\sqrt{2005+2006}^2=2005+2006=4011\)

\(\left(\sqrt{2005}+\sqrt{2006}\right)^2=2005+2\sqrt{2005}.\sqrt{2006}+2006=4011+2\sqrt{2005}.\sqrt{2006}\)

Vì \(2\sqrt{2005}.\sqrt{2006}>0\) nên =>\(4011

ai biết thì giải giúp với 

bằng nhau

\(\sqrt{2004}-\sqrt{2003}=\dfrac{1}{\sqrt{2004}+\sqrt{2003}}\)

\(\sqrt{2006}-\sqrt{2005}=\dfrac{1}{\sqrt{2006}+\sqrt{2005}}\)

Mà \(\sqrt{2004}+\sqrt{2003}< \sqrt{2006}< \sqrt{2005}\)

\(\Rightarrow\dfrac{1}{\sqrt{2004}+\sqrt{2003}}>\dfrac{1}{\sqrt{2006}+\sqrt{2005}}\)

\(\Rightarrow\sqrt{2004}-\sqrt{2003}>\sqrt{2006}-\sqrt{2005}\)

lấy vế đầu trừ vế sau nếu kết quả dương suy ra vế đầu lớn hơn nếu kq âm thì vế sau lớn hơn

có\(\sqrt{2006}-\sqrt{2005}=\frac{\left(\sqrt{2006}-\sqrt{2005}\right)\left(\sqrt{2006}+\sqrt{2005}\right)}{\sqrt{2006}+\sqrt{2005}}\)\(=\frac{1}{\sqrt{2006}+\sqrt{2005}}\)

có\(\sqrt{2005}-\sqrt{2004}=\frac{\left(\sqrt{2005}-\sqrt{2004}\right)\left(\sqrt{2005}+\sqrt{2004}\right)}{\sqrt{2005}+\sqrt{2004}}\)\(=\frac{1}{\sqrt{2005}+\sqrt{2004}}\)

ta lại có 2006>2005\(\Rightarrow\sqrt{2006}>\sqrt{2005}\)có 2005>2004\(\Rightarrow\sqrt{2005}>\sqrt{2004}\)

\(\Rightarrow\sqrt{2006}+\sqrt{2005}>\sqrt{2005}+\sqrt{2004}\)\(\Rightarrow\frac{1}{\sqrt{2006}+\sqrt{2005}}< \frac{1}{\sqrt{2005}+\sqrt{2004}}\)

\(\Rightarrow\sqrt{2006}-\sqrt{2005}>\sqrt{2005}-\sqrt{2004}\)

2) \(-x^2+4x-2\)

\(=-\left(x^2-4x+2\right)\)

\(=-\left(x^2-4x+4-2\right)\)

\(=-\left(x-2\right)^2+2\)

Ta có: \(-\left(x-2\right)^2\le0\forall x\)

\(\Rightarrow-\left(x-2\right)^2+2\le2\forall x\)

Dấu "=" xảy ra:

\(\Leftrightarrow-\left(x-2\right)^2+2=2\Leftrightarrow x=2\)

Vậy: GTLN của bt là 2 tại x=2

b) \(\sqrt{2x^2-3}\) (ĐK: \(x\ge\sqrt{\dfrac{3}{2}}\))

Mà: \(\sqrt{2x^2-3}\ge0\forall x\)

Dấu "=" xảy ra:

\(\sqrt{2x^2-3}=0\Leftrightarrow x=\sqrt{\dfrac{3}{2}}=\dfrac{3\sqrt{2}}{2}\)

Vậy GTNN của bt là 0 tại \(x=\dfrac{3\sqrt{2}}{2}\)

...

1:

b: \(4\sqrt{5}=\sqrt{80}\)

\(5\sqrt{3}=\sqrt{75}\)

=>\(4\sqrt{5}>5\sqrt{3}\)

=>\(\sqrt{4\sqrt{5}}>\sqrt{5\sqrt{3}}\)

c: \(3-2\sqrt{5}-1+\sqrt{5}=2-\sqrt{5}< 0\)

=>\(3-2\sqrt{5}< 1-\sqrt{5}\)

d: \(\sqrt{2006}-\sqrt{2005}=\dfrac{1}{\sqrt{2006}+\sqrt{2005}}\)

\(\sqrt{2005}-\sqrt{2004}=\dfrac{1}{\sqrt{2005}+\sqrt{2004}}\)

\(\sqrt{2006}+\sqrt{2005}>\sqrt{2005}+\sqrt{2004}\)

=>\(\dfrac{1}{\sqrt{2006}+\sqrt{2005}}< \dfrac{1}{\sqrt{2005}+\sqrt{2004}}\)

=>\(\sqrt{2006}-\sqrt{2005}< \sqrt{2005}-\sqrt{2004}\)

e: \(\left(\sqrt{2003}+\sqrt{2005}\right)^2=4008+2\cdot\sqrt{2003\cdot2005}=4008+2\cdot\sqrt{2004^2-1}\)

\(\left(2\sqrt{2004}\right)^2=4\cdot2004=4008+2\cdot\sqrt{2004^2}\)

=>\(\left(\sqrt{2003}+\sqrt{2005}\right)^2< \left(2\sqrt{2004}\right)^2\)

=>\(\sqrt{2003}+\sqrt{2005}< 2\sqrt{2004}\)

Đặt \(a=\sqrt{2006}-\sqrt{2005};b=\sqrt{2006}+\sqrt{2005}\)

Ta có 

\(a=\sqrt{2006}-\sqrt{2005}=\dfrac{\left(\sqrt{2006}-\sqrt{2005}\right)\left(\sqrt{2006}+\sqrt{2005}\right)}{\sqrt{2006}+\sqrt{2005}}=\dfrac{1}{b}\)

\(\RightarrowĐfcm\)

\(\sqrt{2006}-\sqrt{2005}=\dfrac{1}{\sqrt{2006}+\sqrt{2005}}\)

Do đó: \(\sqrt{2006}-\sqrt{2005};\sqrt{2006}+\sqrt{2005}\) là hai số nghịch đảo

hihi cho mình đi

Easy

Ta có:

\(\sqrt{2006}-\sqrt{2005}=\frac{2006-2005}{\sqrt{2006}+\sqrt{2005}}=\frac{1}{\sqrt{2006}+\sqrt{2005}}\)

Tương tự cũng có: \(\frac{1}{\sqrt{2007}+\sqrt{2008}}\)

Dễ thấy: \(\sqrt{2005}+\sqrt{2006}< \sqrt{2007}+\sqrt{2008}\)

\(\Rightarrow\frac{1}{\sqrt{2006}+\sqrt{2005}}>\frac{1}{\sqrt{2007}+\sqrt{2008}}\)

Easy

Ta có:

\(\sqrt{2006}-\sqrt{2005}=\frac{2006-2005}{\sqrt{2006}+\sqrt{2005}}=\frac{1}{\sqrt{2006}+\sqrt{2005}}\)

Tương tự cũng có: \(\frac{1}{\sqrt{2007}+\sqrt{2008}}\)

Dễ thấy: \(\sqrt{2005}+\sqrt{2006}< \sqrt{2007}+\sqrt{2008}\)

\(\Rightarrow\frac{1}{\sqrt{2006}+\sqrt{2005}}>\frac{1}{\sqrt{2007}+\sqrt{2008}}\)

\(\sqrt{2006+2\sqrt{2005}}-\sqrt{2006-2\sqrt{2005}}\)

\(=\sqrt{\left(\sqrt{2005}+1\right)^2}-\sqrt{\left(\sqrt{2005}-1\right)^2}\)

\(=\left(\sqrt{2005}+1\right)-\left(\sqrt{2005}-1\right)\)

= 2

M = \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

\(\Rightarrow\sqrt{2}M\)\(=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\left(\sqrt{7}-1\right)-\left(\sqrt{7}+1\right)\)

= - 2

\(\Rightarrow M=-\sqrt{2}\)