Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có:
n = \(\frac{2003+2004}{2004+2005}\)
\(=>\) n = \(\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)
Vì \(\frac{2003}{2004}>\frac{2003}{2004+2005}\)
\(\frac{2004}{2005}>\frac{2004}{2004+2005}\)
\(=>\frac{2003}{2004}+\frac{2004}{2005}>\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)
\(=>\)m > n
Chúc bạn học tốt :)
\(\frac{x+1}{2004}+1+\frac{x+2}{2003}+1=\frac{x+3}{2002}+1+\frac{x+4}{2001}+1\)
\(\Leftrightarrow\frac{x+2005}{2004}+\frac{x+2005}{2004}-\frac{x+2005}{2003}-\frac{x+2005}{2003}=0\)
\(\Leftrightarrow\left(x+2005\right)\left(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)
\(\Leftrightarrow x+2005=0\Leftrightarrow x=-2005\)
=> (x+1)/2004+1+(x+2)/2003+1=(x+3)/2002+1+(x+4)/2001+1
=> (x+2005)/2004+(x+2005)/2003=(x+2005)/2002+(x+2005)/2001
=> (x+2005)(1/2004+1/2003-1/2002-1/2001)=0
=> x+2005=0
=> x=-2005
Ta có : \(\frac{x^2-2008}{2007}+\frac{x^2-2007}{2006}+\frac{x^2-2006}{2005}=\frac{x^2-2005}{2004}+\frac{x^2-2004}{2003}+\frac{x^2-2003}{2002}\)
=> \(\frac{x^2-2008}{2007}+1+\frac{x^2-2007}{2006}+1+\frac{x^2-2006}{2005}+1=\frac{x^2-2005}{2004}+1+\frac{x^2-2004}{2003}+1+\frac{x^2-2003}{2002}+1\)
=> \(\frac{x^2-2008}{2007}+\frac{2007}{2007}+\frac{x^2-2007}{2006}+\frac{2006}{2006}+\frac{x^2-2006}{2005}+\frac{2005}{2005}=\frac{x^2-2005}{2004}+\frac{2004}{2004}+\frac{x^2-2004}{2003}+\frac{2003}{2003}+\frac{x^2-2003}{2002}+\frac{2002}{2002}\)
=> \(\frac{x^2-1}{2007}+\frac{x^2-1}{2006}+\frac{x^2-1}{2005}=\frac{x^2-1}{2004}+\frac{x^2-1}{2003}+\frac{x^2-1}{2002}\)
=> \(\frac{x^2-1}{2007}+\frac{x^2-1}{2006}+\frac{x^2-1}{2005}-\frac{x^2-1}{2004}-\frac{x^2-1}{2003}-\frac{x^2-1}{2002}=0\)
=> \(\left(x^2-1\right)\left(\frac{1}{2007}+\frac{1}{2006}+\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\right)=0\)
=> \(x^2-1=0\)
=> \(x^2=1\)
=> \(x=\pm1\)
Vậy phương trình có 2 nghiệm là x = 1, x = -1 .
\(B=\dfrac{2005}{x^m}+\dfrac{2003}{x^n}=\dfrac{2004}{x^m}+\dfrac{1}{x^m}+\dfrac{2004}{x^n}-\dfrac{1}{x^n}=A+\left(\dfrac{1}{x^m}-\dfrac{1}{x^n}\right)\)
\(\Rightarrow A< B\)
mình ko bt đúng hay sai nữa
Bài 1:
Ta có: \(\frac{497}{-499}=-\frac{497}{499}>-\frac{499}{499}=-1\left(1\right)\)
\(-\frac{2345}{2341}< -\frac{2341}{2341}=-1\left(2\right)\)
Từ (1) và (2) \(\Rightarrow\frac{497}{-499}>-\frac{2345}{2341}\)
Bài 2:
\(\frac{x+5}{2005}+\frac{x+6}{2004}=\frac{x+7}{2003}+3=0\)
\(\Rightarrow\frac{x+5}{2005}+\frac{x+6}{2004}+\frac{x+7}{2003}+3=0\)
\(\Rightarrow\frac{x+5}{2005}+1+\frac{x+6}{2004}+1+\frac{x+7}{2003}+1=0\)
\(\Rightarrow\frac{x+2010}{2005}+\frac{x+2010}{2004}+\frac{x+2010}{2003}=0\)
\(\Rightarrow\left(x+2010\right)\times\left(\frac{1}{2005}+\frac{1}{2004}+\frac{1}{2003}\right)=0\)
Vì \(\left(\frac{1}{2005}+\frac{1}{2004}+\frac{1}{2003}\right)\ne0\Rightarrow x+2010=0\)
\(\Rightarrow x=0-2010=-2010\)
Vậy x = -2010
\(\frac{x}{6}\)-\(\frac{1}{12}\)=\(\frac{2}{y}\)
\(\rightarrow\)\(\frac{2x}{12}\)-\(\frac{1}{12}\)=\(\frac{2}{y}\)
\(\rightarrow\)\(\frac{2x-1}{12}\)=\(\frac{2}{y}\)
\(\Rightarrow\)(2x-1).y=12.2=24 nên 2x-1 và y\(\in\)Ư(24) mà Ư(24)={1;-1;2;-2;3;-3;4;-4;6;-6;8;-8;12;-12;24;-24}
vì 2x-1 là số lẻ nên 2x-1={+_1;+_3}nên ta có bảng:
| 2x-1 | 1 | -1 | 3 | -3 |
| y | 24 | -24 | 8 | -8 |
| x | 1 | 0 | 2 | -1 |
vậy x,y\(\in\){(1;24)(0;-24)(8;2)(-8;-1)
