x=-2013

cho tao 10 k nha

x-y/2014=x+y/2012=x-y+x+y/2014+2012=2x/2026=x/1013 (theo tc dãy tỉ số bằng nhau)

ta lại có: x+y/2012=x.y/2013=x/2013 (chứng minh trên) => y=1

x-y/2014=x.y/2013=x/2013 => x-1/2014=x/2013

thì (x-1).2013=2014x

    2013x-2013=2014x

   -1x=2013 thì x=-2013

\(\frac{x+4}{2012}+\frac{x+3}{2013}=\frac{x+2}{2014}+\frac{x+1}{2015}\)

=> \(\frac{x+4}{2012}+1+\frac{x+3}{2013}+1=\frac{x+2}{2014}+1+\frac{x+1}{2015}+1\)

=> \(\frac{x+2016}{2012}+\frac{x+2016}{2013}=\frac{x+2016}{2014}+\frac{x+2016}{2015}\)

=> \(\frac{x+2016}{2012}+\frac{x+2016}{2013}-\frac{x+2016}{2014}-\frac{x+2016}{2015}=0\)

=> \(\left(x+2016\right).\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}-\frac{1}{2015}\right)=0\)

Vì \(\frac{1}{2012}>\frac{1}{2014};\frac{1}{2013}>\frac{1}{2015}\)

=> \(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}-\frac{1}{2015}\ne0\)

=> \(x+2016=0\)

=> \(x=-2016\)

Xét x < 2012 ta có :

2012 - x + 2013 - x = 2014 <=> 4025 - 2x = 2014 <=> 2x = 2011 => x = 1005,5

Xét 2012 ≤ x < 2013 ta có : x - 2012 + 2013 - x = 2014 <=> 1 = 2014 ( loại )

Xét x ≥ 2013 ta có :

x - 2012 + x - 2013 = 2014 <=> 2x - 4025 = 2014 <=> 2x = 6039 => x = 3019,5

Vậy x = { 1005,5 ; 3019,5 }