1/(x+2001) - 1/(x+2007) =7/8
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TN
11 tháng 2 2016
\(\Leftrightarrow\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{\left(x+2000\right)\left(x+2007\right)}\)
\(\Rightarrow\frac{7}{\left(x+2000\right)\left(x+2007\right)}=\frac{7}{2^3}\)
\(\Rightarrow\frac{7\left(x^2+4007x+4013992\right)}{8\left(x+2000\right)\left(x+2007\right)}=0\)
áp dụng Delta ta có :
\(\Leftrightarrow x^2+4007x+4013992=0\)
\(\Rightarrow4007^2-4\left(1.4013992\right)=81\)
\(\Rightarrow x_{1,2}=\frac{-b+-\sqrt{D}}{2a}=\frac{-4007+-\sqrt{81}}{2}\)
=>x=-2008 hoặc -1999
NV
0
13 tháng 7 2018
\(\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{8}\)
\(\frac{8\left(x+2007\right)}{8\left(x+2000\right)\left(x+2007\right)}-\frac{8\left(x+2000\right)}{8\left(x+2000\right)\left(x+2007\right)}=\frac{7\left(x+2000\right)\left(x+2007\right)}{8\left(x+2000\right)\left(x+2007\right)}\)
\(8x+8.2007-8x+8.2000=7\left(x^2+4007x+2000.2007\right)\)
\(8.7-7\left(x^2+4007x+2000.2007\right)=0\)
\(7\left(8-x^2-4007x-2000.2007\right)=0\)
\(8-x^2-4007x-2000.2007=0\)
\(x^2+4007x+4013992=0\)
\(\left(x^2+2008x\right)+\left(1999x+4013992\right)=0\)
\(\left(x+2008\right)\left(x+1999\right)=0\)
\(\hept{\begin{cases}x=-2008\\x=-1999\end{cases}}\)
13 tháng 7 2018
\(\frac{1}{\left(x+2000\right)\left(x+2001\right)}+\frac{1}{\left(x+2001\right)\left(x+2002\right)}+\frac{1}{\left(x+2006\right)\left(x+2007\right)}=\frac{7}{8}\)
\(\frac{1}{x+2000}-\frac{1}{x+2001}+\frac{1}{x+2001}-\frac{1}{x+2002}+...+\frac{1}{x+2006}-\frac{1}{x+2007}=\frac{7}{8}\)
\(\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{8}\)
NM
31 tháng 1 2016
\(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
=> \(\frac{1}{x+2000}-\frac{1}{x+2001}+\frac{1}{x+2001}-\frac{1}{x+2002}+....+\frac{1}{x+2006}-\frac{1}{x+2007}=\frac{7}{8}\)
<=> \(\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{8}\)
<=> \(\frac{7}{\left(x+2000\right)\left(x+2007\right)}=\frac{7}{8}\Leftrightarrow\left(x+2000\right)\left(x+2007\right)=8\)
=> x = -1999 hoặc x = - 2008
TC
4
H9
HT.Phong (9A5)
CTVHS
16 tháng 10 2023
\(\dfrac{1}{2001\times2003}+\dfrac{1}{2003\times2005}+...+\dfrac{1}{2011\times2013}\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{2}{2001\times2003}+\dfrac{2}{2003\times2005}+...+\dfrac{2}{2011\times2013}\right)\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2001}-\dfrac{1}{2003}+\dfrac{1}{2003}-...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{1}{2001}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{4}{1342671}\)
\(=\dfrac{2}{1342671}\)
T
16 tháng 10 2023
\(\dfrac{1}{2001\times2003}+\dfrac{1}{2003\times2005}+\dfrac{1}{2005\times2007}+...+\dfrac{1}{2011\times2013}\) (sửa đề)
\(=\dfrac{1}{2}\times\left(\dfrac{2}{2001\times2003}+\dfrac{2}{2003\times2005}+\dfrac{2}{2005\times2007}+...+\dfrac{2}{2011\times2013}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{2001}-\dfrac{1}{2003}+\dfrac{1}{2003}-\dfrac{1}{2005}+\dfrac{1}{2005}-\dfrac{1}{2007}+...+\dfrac{1}{2011}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\times\left(\dfrac{1}{2001}-\dfrac{1}{2013}\right)\)
\(=\dfrac{1}{2}\times\dfrac{4}{1342671}\)
\(=\dfrac{2}{1342671}\)
khó, ai thấy khó thì tick nha
\(\Leftrightarrow\frac{1}{x+2000}-\frac{1}{x+2007}=\frac{7}{\left(x+2000\right)\left(x+2007\right)}\)
\(\Rightarrow\frac{7}{\left(x+2000\right)\left(x+2007\right)}=\frac{7}{2^3}\)
\(\Rightarrow\frac{7\left(x^2+4007x+4013992\right)}{8\left(x+2000\right)\left(x+2007\right)}=0\)
áp dụng Delta ta có :
\(\Leftrightarrow x^2+4007x+4013992=0\)
\(\Rightarrow4007^2-4\left(1.4013992\right)=81\)
\(\Rightarrow x_{1,2}=\frac{-b+-\sqrt{D}}{2a}=\frac{-4007+-\sqrt{81}}{2}\)
=>x=-2008 hoặc -1999