\(\dfrac{x-1001}{1006}+\dfrac{x-1003}{1004}+\dfrac{x-1005}{1002}+\dfrac{x-1007}{1000}=4\)

\(\Rightarrow\dfrac{x-1001}{1006}-1+\dfrac{x-1003}{1004}-1+\dfrac{x-1005}{1002}-1+\dfrac{x-1007}{1000}-1=0\)

\(\Rightarrow\dfrac{x-2007}{1006}+\dfrac{x-2007}{1004}+\dfrac{x-2007}{1002}+\dfrac{x-2007}{1000}=0\)

\(\Rightarrow\left(x-2007\right)\left(\dfrac{1}{1006}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}\right)=0\)

Dễ thấy: \(\dfrac{1}{1000}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}>0\Leftrightarrow x-2007=0\Leftrightarrow x=2007\)

\(\dfrac{x-1001}{1006}+\dfrac{x-1003}{1004}+\dfrac{x-1005}{1002}+\dfrac{x-1007}{1000}=4\)

\(\Leftrightarrow\dfrac{x-1001}{1006}-1+\dfrac{x-1003}{1004}-1+\dfrac{x-1005}{1002}-1+\dfrac{x-1007}{1000}-1=0\)

\(\Leftrightarrow\dfrac{x-2007}{1006}+\dfrac{x-2007}{1004}+\dfrac{x-2007}{1002}+\dfrac{x-2007}{1000}=0\)

\(\Leftrightarrow\left(x-2007\right)\left(\dfrac{1}{1006}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}=0\right)\)

\(\Leftrightarrow x-2007=0\)

\(\Leftrightarrow x=2007\)

Ta có: \(\dfrac{x+1006}{1007}+\dfrac{x+1005}{1008}=\dfrac{x+1004}{1009}+\dfrac{x+1003}{1010}\)

\(\Leftrightarrow\dfrac{x+1006}{1007}+1+\dfrac{x+1005}{1008}+1=\dfrac{x+1004}{1009}+1+\dfrac{x+1003}{1010}+1\)

\(\Leftrightarrow\dfrac{x+2013}{1007}+\dfrac{x+2013}{1008}=\dfrac{x+2013}{1009}+\dfrac{x+2013}{1010}\)

\(\Leftrightarrow\dfrac{x+2013}{1007}+\dfrac{x+2013}{1008}-\dfrac{x+2013}{1009}-\dfrac{x+2013}{1010}=0\)

\(\Leftrightarrow\left(x+2013\right)\left(\dfrac{1}{1007}+\dfrac{1}{1008}-\dfrac{1}{1009}-\dfrac{1}{1010}\right)=0\)

mà \(\dfrac{1}{1007}+\dfrac{1}{1008}-\dfrac{1}{1009}-\dfrac{1}{1010}\ne0\)

nên x+2013=0

hay x=-2013

Vậy: S={-2013}

Ta có:B-A=1001²+1002²+1004²+1007²-1000²-1003²-1005²-1006²

=(1001²-1000)²+(1002²-1003²)+(1004²-1005²)+(1007²-1006²)

=(1001-1000)(1001+1000)+(1002-1003)(1002+1003)+(1004-1005)(1004+1005)+(1007-1006)(1007+1006)

=2001-2005-2009+2013

=0

=>A=B

506521

506521 chúc bạn học tốt

.a, \(\frac{x+1}{999}+\frac{x+2}{998}=\frac{x+3}{997}+\frac{x+4}{996}\)

.\(< =>\frac{x+1}{999}+1+\frac{x+2}{998}+1=\frac{x+3}{997}+1+\frac{x+4}{996}+1\)

.\(< =>\frac{x+1}{999}+\frac{999}{999}+\frac{x+2}{998}+\frac{998}{998}=\frac{x+3}{997}+\frac{997}{997}+\frac{x+4}{996}+\frac{996}{996}\)

.\(< =>\frac{x+1+999}{999}+\frac{x+2+998}{998}=\frac{x+3+997}{997}+\frac{x+4+996}{996}\)

.\(< =>\frac{x+1000}{999}+\frac{x+1000}{998}-\frac{x+1000}{997}-\frac{x+1000}{996}=0\)

.\(< =>\left(x+1000\right)\left(\frac{1}{999}+\frac{1}{998}-\frac{1}{997}-\frac{1}{996}\right)=0\)

.Do \(\frac{1}{999}+\frac{1}{998}-\frac{1}{997}-\frac{1}{996}\ne0\)

.Suy ra \(x+1000=0\Leftrightarrow x=-1000\)

.b, \(\frac{x+1}{1001}+\frac{x+2}{1002}=\frac{x+3}{1003}+\frac{x+4}{1004}\)

.\(< =>\frac{x+1}{1001}-1+\frac{x+2}{1002}-1=\frac{x+3}{1003}-1+\frac{x+4}{1004}-1\)

.\(< =>\frac{x+1}{1001}-\frac{1001}{1001}+\frac{x+2}{1002}-\frac{1002}{1002}=\frac{x+3}{1003}-\frac{1003}{1003}+\frac{x+4}{1004}-\frac{1004}{1004}\)

.\(< =>\frac{x+1-1001}{1001}+\frac{x+2-1002}{1002}=\frac{x+3-1003}{1003}+\frac{x+4-1004}{1004}\)

.\(< =>\frac{x-1000}{1001}+\frac{x+1000}{1002}-\frac{x+1000}{1003}-\frac{x+1000}{1004}=0\)

.\(< =>\left(x-1000\right)\left(\frac{1}{1001}+\frac{1}{1002}-\frac{1}{1003}-\frac{1}{1004}\right)=0\)

.Do \(\frac{1}{1001}+\frac{1}{1002}-\frac{1}{1003}-\frac{1}{1004}\ne0\)

.Suy ra \(x-1000=0\Leftrightarrow x=1000\)

cảm ơn

mình làm luộn 2 câu còn lại nhé ^^

.c,\(|x|-\frac{15}{2}=\frac{15}{4}\)

.\(< =>|x|=\frac{15}{4}+\frac{15}{2}=\frac{15}{4}+\frac{30}{4}=\frac{45}{4}\)

.\(< =>\orbr{\begin{cases}x=\frac{45}{4}\\x=-\frac{45}{4}\end{cases}}\)

.d,\(|\frac{3}{4}-x|+1=\frac{3}{2}\)

.\(< =>|\frac{3}{4}-x|=\frac{3}{2}-1=\frac{3}{2}-\frac{2}{2}=\frac{1}{2}\)

.\(< =>\orbr{\begin{cases}\frac{3}{4}-x=\frac{1}{2}\\\frac{3}{4}-x=-\frac{1}{2}\end{cases}< =>\orbr{\begin{cases}x=\frac{3}{4}-\frac{1}{2}=\frac{1}{4}\\x=\frac{3}{4}+\frac{1}{2}=\frac{5}{4}\end{cases}}}\)

\(\frac{x-1003}{1007}+\frac{x-4}{1003}+\frac{x+2010}{1005}=7\)

\(\Rightarrow\left(\frac{x-1003}{1007}-1\right)+\left(\frac{x-4}{1003}-1\right)+(\frac{x+2010}{1005}-4)=0\)

\(\Rightarrow\frac{x-2010}{1007}+\frac{x-2010}{1003}+\frac{x-2010}{1005}=0\)

\(\Rightarrow\left(x-2010\right)\left(\frac{1}{1007}+\frac{1}{1003}+\frac{1}{1005}\right)\)

Vì

\(\frac{1}{1007}+\frac{1}{1003}+\frac{1}{1005}\ne0\Rightarrow X-2010=0\Rightarrow x=2010\)

\(\frac{x-1003}{1007}+\frac{x-4}{1003}+\frac{x+2010}{1005}=7\)

\(\frac{x-1003}{1007}-1+\frac{x-4}{1003}-2+\frac{x+2010}{1005}-4=0\)

\(\frac{x-2010}{1003}+\frac{x-2010}{1005}+\frac{x-2010}{1007}=0\)

\(\left(x-2010\right)\left(\frac{1}{1003}+\frac{1}{1005}+\frac{1}{1007}\right)=0\)

\(\frac{1}{1003}+\frac{1}{1005}+\frac{1}{1007}\ne0\)

\(\Rightarrow x-2010=0\Rightarrow x=2010\)