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\(\Rightarrow\frac{x+5}{2015}+1+\frac{x+4}{2016}+1+\frac{x+3}{2017}+1=\frac{x+2015}{5}+1+\frac{x+2016}{4}+1+\frac{x+2017}{3}+1\)
\(\Rightarrow\frac{x+2020}{2015}+\frac{x+2020}{2016}+\frac{x+2020}{2017}=\frac{x+2020}{5}+\frac{x+2020}{4}+\frac{x+2020}{3}\)
\(\Rightarrow\left(x+2020\right)\left(\frac{1}{2015}+\frac{1}{2016}+\frac{1}{2017}-\frac{1}{5}-\frac{1}{4}-\frac{1}{3}\right)=0\)
\(\Rightarrow x=-2020\)
\(\frac{x+2}{2018}+\frac{x+3}{2017}+\frac{x+4}{2016}=-3\)
\(\Rightarrow\left(\frac{x+2}{2018}+1\right)+\left(\frac{x+3}{2017}+1\right)+\left(\frac{x+4}{2016}+1\right)=0\)
\(\Rightarrow\frac{x+2020}{2018}+\frac{x+2020}{2017}+\frac{x+2020}{2016}=0\)
\(\Rightarrow\left(x+2020\right).\left(\frac{1}{2018}+\frac{1}{2017}+\frac{1}{2016}\right)=0\)
\(\Rightarrow x+2020=0\Rightarrow x=2020\)
Ta có :
\(\left|x-2016\right|+2016=x\)
\(\Leftrightarrow\)\(\left|x-2016\right|=x-2016\)
+) Nếu \(x-2016\ge0\)\(\Rightarrow\)\(x\ge2016\) ta có :
\(x-2016=x-2016\)
\(\Leftrightarrow\)\(x=x\) ( thoã mãn với mọi x )
+) Nếu \(x-2016< 0\)\(\Rightarrow\)\(x< 2016\) ta có :
\(-\left(x-2016\right)=x-2016\)
\(\Leftrightarrow\)\(-x+2016=x-2016\)
\(\Leftrightarrow\)\(-x-x=-2016-2016\)
\(\Leftrightarrow\)\(-2x=-4032\)
\(\Leftrightarrow\)\(x=\dfrac{-4032}{-2}\)
\(\Leftrightarrow\)\(x=2016\) ( loại )
Vậy \(x\ge2016\)
Chúc bạn học tốt ~
cảm ơn