Tìm x biết, (x-1)/ 2004 + (x-2)/ 2003 - (x-1) / 2002= (x-4)/ 2001
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QQ
5
1 tháng 8 2015
\(\left(x-\frac{1}{2004}\right)+\left(x-\frac{2}{2003}\right)-\left(x-\frac{3}{2002}\right)=x-\frac{4}{2001}\)
\(x-\frac{1}{2004}+x-\frac{2}{2003}-x+\frac{3}{2002}-x=-\frac{4}{2001}\)
\(x+x-x-x-\frac{1}{2004}-\frac{2}{2003}+\frac{3}{2002}=-\frac{4}{2001}\)
\(0x-\frac{1}{2004}-\frac{2}{2003}+\frac{3}{2002}=-\frac{4}{2001}\)
\(\Rightarrow\) Vô lý
Vậy \(x\in\phi\)
V
1
V
1
QQ
0
DP
3 tháng 8 2017
\(\frac{x+4}{2001}+\frac{x+3}{2002}=\frac{x+2}{2003}+\frac{x+1}{2004}\)
\(\Leftrightarrow\left(\frac{x+4}{2001}+1\right)+\left(\frac{x+3}{2002}+1\right)=\left(\frac{x+2}{2003}+1\right)+\left(\frac{x+1}{2004}+1\right)\)
\(\Leftrightarrow\frac{x+2005}{2001}+\frac{x+2005}{2002}=\frac{x+2005}{2003}+\frac{x+2005}{2004}\)
\(\Leftrightarrow\frac{x+2005}{2001}+\frac{x+2005}{2002}-\frac{x+2005}{2003}-\frac{x+2005}{2004}=0\)
\(\Leftrightarrow\left(x+2005\right).\left(\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}+\frac{1}{2004}\right)=0\)
Vì \(\left(\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}+\frac{1}{2004}\right)\ne0\)
\(\Rightarrow x+2004=0\)
\(\Rightarrow x=0-2004=-2004\)
QQ
6
14 tháng 1 2016
x+4/2000+1+x+3/2001+1=x+2/2002+1+x+1/2... y cho nay la cong voi 1/1 chu lkhong phai la cong 1 o duoi mau dau nhe) quy dong chuyen ve ta duoc:
x+2004/2000+x+2004/2001-x+2004/2002-x+...
(x+2004)(1/2000+1/2001-1/2002-1/2003)=...
do 1/2000+1/2001-1/2002-1/2003 luon lon hon 0 nen suy ra:
x+2004=0 suy ra x=-2004
14 tháng 1 2016
x+4/2000+1+x+3/2001+1=x+2/2002+1+x+1/2... y cho nay la cong voi 1/1 chu lkhong phai la cong 1 o duoi mau dau nhe) quy dong chuyen ve ta duoc:
x+2004/2000+x+2004/2001-x+2004/2002-x+...
(x+2004)(1/2000+1/2001-1/2002-1/2003)=...
do 1/2000+1/2001-1/2002-1/2003 luon lon hon 0 nen suy ra:
x+2004=0 suy ra x=-2004
4 tháng 10 2016
\(\frac{x-1}{2004}+\frac{x-2}{2003}=\frac{x-3}{2002}+\frac{x-4}{2001}\)
\(\Rightarrow\frac{x-1}{2004}-1+\frac{x-2}{2003}-1=\frac{x-3}{2002}-1+\frac{x-4}{2001}-1\)
\(\Rightarrow\frac{x-2005}{2004}+\frac{x-2005}{2003}=\frac{x-2005}{2002}+\frac{x-2005}{2001}\)
\(\Rightarrow\frac{x-2005}{2001}+\frac{x-2005}{2002}-\frac{x-2005}{2003}-\frac{x-2005}{2004}=0\)
\(\Rightarrow\left(x-2005\right).\left(\frac{1}{2001}+\frac{1}{2002}-\frac{1}{2003}-\frac{1}{2004}\right)=0\)
Vì \(\frac{1}{2001}>\frac{1}{2003};\frac{1}{2002}>\frac{1}{2004}\)
\(\Rightarrow\frac{1}{2001}+\frac{1}{2002}-\frac{1}{2003}-\frac{1}{2004}\ne0\)
\(\Rightarrow x-2005=0\)
\(\Rightarrow x=2005\)
NT
1
25 tháng 2 2018
=> ( x-2001/2 + ) + ( x-2002/3 + 1 ) = ( x-2003/4 + 1 ) + ( x-2004/5 + 1 )
=> x-1999/2 + x-1999/3 = x-1999/4 + x-1999/5
=> x-1999/2 + x-1999/3 - x-1999/4 - x-1999/5 = 0
=> (x-1999).(1/2+1/3-1/4-1/5) = 0
=> x-1999=0 ( vì 1/2+1/3-1/4-1/5 > 0 )
=> x = 1999
Vậy x = 1999
Tk mk nha
CB
1
23 tháng 9 2016
\(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}=\frac{x-4}{2001}\)
=> \(\frac{x-1}{2004}+\frac{x-2}{2003}-\frac{x-3}{2002}-\frac{x-4}{2001}=0\)
=> \(\left(\frac{x-1}{2004}-1\right)+\left(\frac{x-2}{2003}-1\right)-\left(\frac{x-3}{2002}-1\right)-\left(\frac{x-4}{2001}-1\right)=0\)
=> \(\frac{x-2005}{2004}+\frac{x-2005}{2003}-\frac{x-2005}{2002}-\frac{x-2005}{2001}=0\)
=> \(\left(x-2005\right).\left(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\right)=0\)
Vì \(\frac{1}{2004}< \frac{1}{2002}\); \(\frac{1}{2003}< \frac{1}{2001}\)
=> \(\frac{1}{2004}+\frac{1}{2003}-\frac{1}{2002}-\frac{1}{2001}\ne0\)
=> \(x-2005=0\)
=> \(x=2005\)
Vậy \(x=2005\)