Question

So sánh: \(\sqrt{2008}+\sqrt{2009}+\sqrt{2010}\) và \(\sqrt{2005}+\sqrt{2007}+\sqrt{2015}\)

Answer 1

Ta có

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

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

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

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

Answer 2

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

k và kb với mình nha !!!

Answer 3

tính cụ thể từng cái ra

Answer 4

So sánh $A= \sqrt{2008}+\sqrt{2009}+\sqrt{2010}$ và $B= \sqrt{2005}+\sqrt{2007}+\sqrt{2015}$ - Đại số - Diễn đàn Toán học

Answer 5

Ta có:

\(A=\sqrt{2008}+\sqrt{2009}+\sqrt{2010}-\sqrt{2005}-\sqrt{2007}-\sqrt{2015}\)

\(=\frac{3}{\sqrt{2008}+\sqrt{2005}}+\frac{2}{\sqrt{2009}+\sqrt{2007}}-\frac{5}{\sqrt{2010}+\sqrt{2015}}\)

\(=\left(\frac{3}{\sqrt{2008}+\sqrt{2005}}-\frac{3}{\sqrt{2010}+\sqrt{2015}}\right)+\left(\frac{2}{\sqrt{2007}+\sqrt{2009}}-\frac{2}{\sqrt{2010}+\sqrt{2015}}\right)>0\)

\(A>0\Rightarrow\sqrt{2008}+\sqrt{2009}+\sqrt{2010}>\sqrt{2005}+\sqrt{2007}+\sqrt{2015}\)

Answer 6

Coi Căn thức đầu tiên là A và căn thức tiếp theo là B

A=2008+2009+2010" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:14.04px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">A=2008+2009+2010 và B=2005+2007+2015

2008+2005&lt;2015+2009" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">2008+2005<2015+2009, 2010+2007<2015+2009, 

12008+2005+12010+2007&gt;22015+2009" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">12008+2005+12010+2007>22015+2009.

2008&#x2212;20053+2010&#x2212;20073&gt;2(2015&#x2212;2009)6" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">2008−20053+2010−20073>2(2015−2009)6.

A&gt;B" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-spacing:normal; word-wrap:normal" class="MathJax_CHTML mjx-chtml">A>B

Answer 7

Ta có

{

√2008+√2005<√2015+√2009(1)

√2010+√2007<√2015+√2009(2)

⇒1√2008+√2005 +1√2010+√2007 >2√2015+√2009 

⇔√2008−√20053 +√2010−√20073 >√2015−√20093 

⇔√2008+√2009+√2010>√2005+√2007+√2015

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